Prof. S. Sivaprasad Kumar

Room No. 117, Department of Applied mathematics, AB-03, DTU

Phone:3048
Email: spkumar@dce.ac.in

Qualifications

M.Sc., M.Phil., Ph.D.

Areas of Interest

Complex Analysis

Google Scholar Link

Research Gate

Clarivate

Research Profile:   

Broad area: Complex analysis   

Specialization: Univalent function theory

It is one of the fascinating branches of complex Analysis, where the study of univalent functions reveals numerous intriguing properties through straightforward geometric analysis. As a cornerstone of geometric function theory, this classical subject remains relevant and extends its influence into an ever-expanding array of disciplines, including contemporary mathematical physics, traditional fields like fluid dynamics, nonlinear integrable systems theory, and the study of partial differential equations

Current Focus: Differential Subordinations, Coefficient and radius problems 

The notion of subordination serves as the complex plane's counterpart to inequalities on the real line. In essence, subordination is established by the inclusion of regions. Differential subordination can be viewed as an expansion of differential inequalities,

  • Differential Subordinations – A technique where an analytic function is compared to another through subordination, ensuring that the image of one function lies within the image of another. This approach is used to derive conditions guaranteeing properties such as starlikeness, convexity, and close-to-convexity.

  • Coefficient Problems – Focus on estimating the Taylor or Maclaurin series coefficients of analytic/univalent functions, often to find sharp bounds related to geometric properties or inclusion in specific subclasses.

  • Radius Problems – Determine the largest radius within which a function satisfies certain geometric conditions (e.g., starlike, convex, close-to-convex), providing precise geometric control in the unit disk.

RESEARCH GUIDANCE

Ph.D.  Pursuing :

Ph.D. (Thesis Submitted) :

1. Neha JRF-DTU(FT),DTU, 2021-2024

Title of the Thesis: Coefficient, Radius, and Subordination Problems for Some

Analytic Functions.

 

Ph.D. (Awarded) :

1. Virendra Kumar, JRF-DTU(FT), DTU, 2010 –2015  

Title of the Thesis: Differential subordination, Coefficients estimate and Radius constants of certain analytic functions.

2. Kanika Khatter, UGC NET(FT), DTU, 2014-2018 (Jointly with Prof. V. Ravichandran, DU). 

Title of the Thesis: Coefficient Estimates and Subordination for Univalent Functions

3. Shagun Banga SRF-DST(FT), DTU, 2017-22  

Title of Thesis: Coefficient Estimates and Special Differential Subordinations of Certain Analytic Functions

4.       Priyanka Goel SRF-CSIR(FT), DTU, 2017-23

Title of Thesis: Radius Estimates and Certain Differential Subordinations for Analytic Functions

5.    Kamaljeet SRF-UGC(FT), DTU, 2018-23

Title of Thesis: Radius, Coefficient Constants, and Differential Subordinations of Certain Univalent Functions

6. Surya Giri SRF-UGC(FT), DTU, 2020-2024

Title of the Thesis: Subordination, Inequalities, and Radius Constants of Certain Analytic Functions.

7.  Pooja Yadav SRF-CSIR(FT), DTU, 2018-2025

Title of the Thesis: Subordination and Radius Results for Certain Analytic Functions.

8. Mridula Mundalia JRF-DTU(FT), DTU, 2016-2025

Title of the Thesis: Coefficient Estimates, Radius Constants and Subordination of Certain Analytic Functions.

Research Projects/Dissertation Guidance:

M.Sc.(Dissertation)

1. Snehal (2K22/MSCMAT/43) and Arya Tripathi (2K22/MSCMAT/56), Estimates of Second Hankel Determinents of Logerthmic Coefficients, 2024

2. Vishal Raj Yadav (2K23/MAT/47), Some Coefficient Problems for a Class of Starlike Functions, May, 2025

B.Tech. (Project)

 1. Kush Arora 2K16/MC/47,  Starlike Functions associated with a Petal Shaped Domain, May, 2020.

 2. KHANAK BORAD (2K20/EP/064), Special Subclass of Starlike Functions and an Approach to Differential Subordination throught Loewner Chain, May 2024

Papers communicated to Journals & Available in Arxiv :

  1. Surya Giri and S. S. Kumar, Sharp Estimate of Fifth Coefficient for Ma Minda Starlike
    and Convex Functions,   A1
  2. K. Gangania and S.S. Kumar, On Certain Generalizations of $mathcal{S}^*(psi): II$,   A2
  3. Surya Giri and S. S. Kumar, Radius and Convolution problems of analytic functions involving Semigroup Generators,  A3

  4. P. Goel and S.S. Kumar, Radius Constants of Sigmoid Starlike Functions,  A4

  5.  S.S. Kumar and Neha Verma, Coefficient problems for starlike functions associated with a petal-shaped domain,  A5

  6.  Surya Giri and S. S. Kumar,  Toeplitz determinants on bounded starlike circular domain in $mathbb{C}^n$  A6

  7. Mridula Mundalia and S. S. Kumar,  On a Class of Non-Univalent functions Associated with a Parabolic Region, A7

  8. Surya Giri and S. S. Kumar, Toeplitz determinants of Logarithmic coefficients for Starlike and Convex functions,  A8

  9. S. S. Kumar, Pooja Yadav, A new differential subordination technique for a subclass of starlike functions,   A9

  10.  S. S. Kumar and Surya Giri, Starlike Functions Associated with a Non-Convex Domain,  A10

  11. Neha Verma, and S.S. Kumar, Applications of higher-order differential subordinations to starlikeness and univalence. A11

Papers Published/accepted in Journals [SCIE, Non-SCIE]

Accepted [3]

  1. S. Sivaprasad Kumar, Pooja Yadav, On Starlike Functions Associated with a Bean Shaped Domain, Iranian Journal of Science.  (SCIE, IF-1.553).  A72

  2. S. Sivaprasad Kumar and Pooja Yadav, On applications of extended Jack's lemma, Ukrainian Mathematical Journal, (SCIE, IF-0.5),  A71

  3. Surya Giri and  S. Sivaprasad Kumar, Coefficient Functional and Bohr-Rogosinski Phenomenon for Analytic functions involving Semigroup Generators, Rocky Mountain Journal of Mathematics  {SCIE, IF-0.568). A70

2025 [6]

  1. S. Sivaprasad Kumar, Tripathi, A. & Pannu, S,  On Coefficient Problems for $S^*_{ ho}$, Bull. Iran. Math. Soc. 51, 50 (2025). https://doi.org/10.1007/s41980-025-00979-z (SCIE, IF-0.7). P69

  2. Neha Verma, and S. Sivaprasad Kumar,  On Sharp Bound of Third Hankel determinant for certain starlike functions$ S^*_(alpha)$, Mathematical Methods in the Applied Sciences, 2025; 0: 1–9   https://doi.org/10.1002/mma.11091 (SCIE, IF-2.1).  P68

  3. S. Sivaprasad Kumar and N. Verma, Second and third order differential subordination for exponential function, Bull. Korean Math. Soc. {f 62} (2025), no.~2, 455--467; https://doi.org/10.4134/BKMS.b240148  (SCIE, IF-0.502)   P67

  4. S. Sivaprasad Kumar and Mridula Mundalia, "On Sharp Radius estimates for $mathcal{S}^{*}(eta)$ and a product function", DOI: 10.1515/ms-2025-0022 Math. Slovaca 75 (2025), No. 2, 281{300, (SCIE, IF-1.6).  P66

  5. S. Sivaprasad Kumar, and N. Verma, On Estimation of Hankel Determinants for Certain Class of Starlike Functions, Filomat 39:12 (2025), 3907- 3930 https://doi.org/10.2298/FIL2512907K   (SCIE, IF-0.8). P65

  6. Kumar, S. Sivaprasad, and Mridula Mundalia. “Sufficient Conditions for Starlikeness Related to a Hyperbolic Cosine Function”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 2, Apr. 2025, pp. 159–160,  https://doi.org/10.3842/umzh.v77i2.8382 (SCIE, IF-0.5).  A64

2024 [15]

  1. S. Sivaprasad Kumar and Goel, P. Sufficient Conditions and Radius Problems for the Silverman Class. Ukr Math J 76, 453–473 (2024). https://doi.org/10.1007/s11253-024-02331-w{SCIE, IF-0.464).  A63

  2. S. Sivaprasad Kumar and N. Verma, On a subclass of starlike functions associated with a strip domain, Ukrainian Mathematical Journal,  76 (2024), no.12, 1783--1801 (SCIE, IF-0.5) https://doi.org/10.3842/umzh.v76i12.8000.   P62

  3. S. Sivaprasad Kumar and S. Banga, On a  Special Type of Ma-Minda function, Applied Mathematics-A Journal of Chinese Universities, 2024, 39(4): 654-673 (SCIE, IF-1.2),   https://doi.org/10.1007/s11766-024-4660-0.  P61 DTURE Award-2024
  4. Shanmugam, S. K., & Neha Verma. (2024). Certain coefficient problems of S*e and Ce. Tamkang Journal of Mathematics.  2024 (ESCI, IF-0.46)   https://doi.org/10.5556/j.tkjm.56.2025.5182.  P60

  5. K. Gangania and S. Sivaprasad Kumar, Majorization for Starlike and Convex functions with respect to Conjugate points, Filomat 38:15 (2024), 5239–5246 https://doi.org/10.2298/FIL2415239G (SCIE, IF-0.8)  P59

  6. S. Sivaprasad Kumar and N. Verma, Higher order differential subordinations for certain starlike functions, Bull. Belg. Math. Soc. Simon Stevin 31 (2024), 384–405 2403.17563.pdf (arxiv.org) (SCIE, IF-0.633)  P58

  7. Gangania, Kamaljeet and Kumar, S. Sivaprasad. "Certain radii problems for ?∗(ψ) and special functions" Mathematica Slovaca, vol. 74, no. 1, 2024, pp. 69-90. https://doi.org/10.1515/ms-2024-0006 (SCIE, IF-1.6).  P57
  8. S. Sivaprasad Kumar, Khan, M.G., Ahmad, B. et al. A class of analytic functions associated with sine hyperbolic functions. J Anal 32, 3065–3085(2024). https://doi.org/10.1007/s41478-024-00783-8, (ESCI, SCOPUS, IF-0.8). P56

  9. Giri, S., S. Sivaprasad Kumar, Toeplitz determinants in one and higher dimensions. Acta Math Sci 44, 1931–1944 (2024). https://doi.org/10.1007/s10473-024-0517-0, (SCIE, IF-1.0). P55 DTURE Award-2024

  10. S. Sivaprasad Kumar, Yadav, P. On a Class of Certain Non-univalent Functions. Iran J Sci (2024). https://doi.org/10.1007/s40995-024-01614-y (SCIE, IF-1.4).  P54 DTURE Award-2024

  11. N. Verma & S. Sivaprasad Kumar (2024) Differential subordination of certain class of starlike functions, Complex Variables and Elliptic Equations, https://doi.org/10.1080/17476933.2024.2326833 (SCIE, IF-1.04).  P53

  12. Goel, P., and S. Sivaprasad Kumar, On sharp bounds of certain close-to-convex functions. Afr. Mat. 35, 37 (2024). https://doi.org/10.1007/s13370-024-01176-7  (ESCI, SCOPUS, IF-1.1).  P52

  13. Surya Giri and S. Sivaprasad Kumar, Sharp Bounds of Fifth Coefficient and Hermitian-Toeplitz determinants for Sakaguchi Classes, Bull. Korean Math. Soc. 61 (2024), No. 2, pp. 317–333, https://doi.org/10.4134/BKMS.b230018 (SCIE, IF-0.502). P51

  14. Yadav, P. and S. Sivaprasad Kumar. Partial sums for a generalized class of analytic functions. J Anal (2024). https://doi.org/10.1007/s41478-023-00699-9, (ESCI, SCOPUS, IF-0.8).  P50

  15.  S. Sivaprasad Kumar and P. Goel, On a Generalized Briot-Bouquet type Differential Subordination, Rocky Mountain Journal of Mathematics, Volume 54 (2024), No. 1, 207–226, https://www.doi.org/rmj.2024.54-1  {SCIE, IF-0.568). P49

2023 [10]

  1. Giri, S., S. Sivaprasad Kumar. Toeplitz Determinants for a Class of Holomorphic Mappings in Higher Dimensions. Complex Anal. Oper. Theory 17, 86  (2023).  https://doi.org/10.1007/s11785-023-01394-0  (SCIE, IF-0.8).  P48

  2. Giri, S., S. Sivaprasad Kumar. Toeplitz determinants for a subclass of quasi-convex mappings in higher dimensions. J Anal (2023). https://doi.org/10.1007/s41478-023-00625-z (ESCI, SCOPUS, IF-0.8).  P47

  3. Giri, S., S. Sivaprasad Kumar. Hermitian–Toeplitz determinants for certain univalent functions. Anal.Math.Phys. 13, 37 (2023). https://doi.org/10.1007/s13324-023-00800-2 (SCIE, IF-1.570).DTURE Award-2023  P46
  4. Shagun Banga . S. Sivaprasad Kumar. "A novel subclass of starlike functions." Adv. Studies: Euro-Tbilisi Math. J. 16 (3) 11 - 32, September 2023. https://doi.org/10.32513/asetmj/193220082322 (SCOPUS)  P45
  5. Mundalia, M., S. Sivaprasad Kumar On a subfamily of starlike functions related to hyperbolic cosine function. J Anal (2023). https://doi.org/10.1007/s41478-023-00550-1 (ESCI, SCOPUS, IF-0.8).  P44
  6. Mundalia, M., S. Sivaprasad Kumar. Coefficient Problems for Certain Close-to-Convex Functions. Bull. Iran. Math. Soc. 49, 5 (2023).  https://doi.org/10.1007/s41980-023-00751-1 {SCIE, IF-0.776) . P43

  7. Verma, Neha; Kumar, S. Sivaprasad, A Conjecture on $H_3(1)$ for Certain Starlike Functions.Math. Slovaca73(2023), no.5, 1197–1206, https://doi.org/10.1515/ms-2023-0088, {SCIE, IF-1.6).  P42

  8. Gangania, Kamaljeet; S. Sivaprasad Kumar,  A generalized Bohr-Rogosinski phenomenon, Iran.  J. Sci.
    47(2023), no.1, 187–198.      https://doi.org/10.1007/s40995-022-01398-z. (SCIE, IF-1.553).  P41

  9.  Banga, Shagun; Kumar, Shanmugam Sivaprasad, Sharp bounds of third Hankel determinant for a class of starlike functions and a subclass of q-starlike functions, Khayyam J. Math.9(2023), no.1, 38–53, https://www.kjm-math.org/article_164407.html#:~:text=10.22034/KJM.2022.350982.2597,  (SCOPUS).  P40
  10. S. Sivaprasad Kumar and Pooja Yadav, On Oblique Domains of Janowski Function, Math. Slovaca 73 (2023), No. 2, 407-424 (SCIE, IF-1.6), https://doi.org/10.1515/ms-2023-0031  P39

2022 [6]

  1. Shanmugam Sivaprasad Kumar. Priyanka Goel. "Application of Pythagorean means and Differential Subordination." Bull. Belg. Math. Soc. Simon Stevin 29 (3) 285 - 305, December 2022. https://doi.org/10.36045/j.bbms.210605. {SCIE, IF-0.633).  A38
  2.  K.Gangania and S. Sivaprasad Kumar, $mathcal{S}^*(psi)$ and $mathcal{C}(psi)$-radii for some special functions,   Iran. J. Sci. Technol. Trans. A Sci.  46, 955–966 (2022). https://doi.org/10.1007/s40995-022-01313-6. {SCIE, IF-1.553).  DTURE Award-2022  P37
  3. K. Gangania and S. Sivaprasad Kumar, Bohr radius for some classes of Harmonic mappings, Iran. J. Sci. Technol. Trans. A Sci. 46, 883–890 (2022). (SCIE, IF-1.553)https://doi.org/10.1007/s40995-022-01304-7.  DTURE Award-2022  P36
  4. Kush Arora and S. Sivaprasad Kumar, Starlike Functions associated with a Petal Shaped Domain, Bull. Korean Math. Soc. 59 (2022), No. 4, pp. 993-1010 (SCIE, IF 0.502) https://doi.org/10.4134/BKMS.b210602  P35
  5. K. Gangania and S. Sivaprasad Kumar, Bohr-Rogosinski phenomenon for $mathcal{S}^*(psi)$ and $mathcal{C}(psi)$,  Mediterranean Journal of Mathematics,  19, 161 (2022). https://doi.org/10.1007/s00009-022-02074-7. { SCIE, IF-1.400}  DTURE Award-2022  P34
  6. K. Gangania and S. Sivaprasad Kumar, On Certain Generalizations of $mathcal{S}^*(psi)$,  Comput. Methods Funct. Theory.   22, 215–227 (2022).   (SCIE, IF-1.155) https://doi.org/10.1007/s40315-021-00386-5.  DTURE Award-2022  P33

2021 [3]

  1. S. Sivaprasad Kumar and K. Gangania, On geometrical properties of certain analytic functions,  Iranian Journal of Science and Technology, Transactions A: Science, 45, 1437–1445 (2021). (SCIE, IF-1.553) https://doi.org/10.1007/s40995-021-01116-1. DTURE Award-2021  P32
  2. S. Sivaprasad Kumar and S. Banga, On Certain Exact Differential Subordinations Involving Convex Dominants, Mediterranean Journal of Mathematics, 18, 260 (2021). (SCIE, IF-1.4) https://doi.org/10.1007/s00009-021-01895-2. DTURE Award-2021  P31
  3. S. Sivaprasad Kumar, Kamaljeet, G. A cardioid domain and starlike functions. Anal.Math.Phys. 11, 54 (2021). (SCIE, IF-2.056) https://doi.org/10.1007/s13324-021-00483-7 DTURE Award-2021 P30

2020 [5]

  1. S. Sivaprasad Kumar, Priyanka Goel,  Starlike functions and higher order differential subordinations. RACSAM 114, 192 (2020).  (SCIE-, IF-1.406)   https://doi.org/10.1007/s13398-020-00925-0 DTURE Award-2020  P29
  2. S. Banga and S. Sivaprasad Kumar, The sharp bounds of the second and third Hankel determinants for the class SL*, Math. Slovaca {f 70} (2020), no.~4, 849--862. (SCIE, IF-0.654)      https://doi.org/10.1515/ms-2017-0398.  P28
  3. S. Banga and S. Sivaprasad. Kumar, Applications of differential subordinations to certain classes of starlike functions, J. Korean Math. Soc. {f 57} (2020), no.~2, 331--357. (SCIE, IF-0.630)      https://doi.org/10.4134/JKMS.j190051  P27
  4. P. Goel and S. Sivaprasad Kumar, Certain class of starlike functions associated with modified sigmoid function, Bull. Malays. Math. Sci. Soc. {f 43} (2020), no.~1, 957--991. (SCIE, IF-0.856)       https://doi.org/10.1007/s40840-019-00784-y  P26
  5. K. Khatter, V. Ravichandran and S. Sivaprasad Kumar, Third Hankel determinant of starlike and convex functions, J. Anal. {f 28} (2020), no.~1, 45—56     https://doi.org/10.1007/s41478-017-0037-6  P25

Before 2020

  1. NakEun Cho, Virendra Kumar, S. Sivaprasad Kumar, V. Ravichandran, Radius problems for starlike functions associated with the sine function, Bull. Iranian Math. Soc. {f 45} (2019), no.~1, 213--232 (SCIE IF- 0.287) https://doi.org/10.1007/s41980-018-0127-5  P24
  2. K. Khatter, V. Ravichandran and S. Sivaprasad Kumar, Starlike functions associated with exponential function and the lemniscate of Bernoulli, Rev. R. Acad. Cienc. Exactas F'{i}s. Nat. Ser. A Mat. RACSAM {f 113} (2019), no.~1, 233--253.. SCIE (IF- 1.074) https://doi.org/10.1007/s13398-017-0466-8  P23
  3. K. Khatter, S. K. Lee and S. Sivaprasad. Kumar, Coefficient bounds for certain analytic functions, Bull. Malays. Math. Sci. Soc. {f 41} (2018), no.~1, 455--490.. SCIE (IF-0.84) https://doi.org/10.1007/s40840-016-0414-3  P22
  4. Ali, Rosihan M.; Kumar, Virendra; Ravichandran, V., S.Sivaprasad Kumar. Radius of starlikeness for analytic functions with fixed second coefficient. Kyungpook Math. J.57 (2017), no. 3, 473--492. SCOPUS https://doi.org/10.5666/KMJ.2017.57.3.473  P21
  5. Virendra Kumar and S. Sivaprasad Kumar, "On Certain Properties of Meromorphic Multivalent Functions Defined by a Generalized Differential Operator", Acta Universitatis Apulensis, No.47(2016). 147-158.  https://doi.org/10.17114/j.aua  P20
  6. S. Sivaprasad Kumar and Virendra Kumar, "On the Fekete-Szego inequality for Certain class of analytic functions", Acta Universitatis Apulensis, No.37(2014). 211-222   auajournal.uab.ro/upload/62_1020_sv3.pdf  P19
  7. S. Sivaprasad Kumar, Virendra Kumar, and V. Ravichandran, “Estimates for the initial coefficients of bi-univalent functions”, Tamsui Oxford J. of Inform. and Math. Sci. 29(4), 2013, 487-504 https://mathscinet.ams.org/mathscinet-getitem?mr=3363640  P18
  8. Sivaprasad Kumar S, Kumar Virendra, Ravichandran V and Cho NakEun, “Sufficient Conditions for Starlike Functions Associated with the Lemniscate of Bernoulli”, Journal of Inequalities and Applications (Springer), 2013, 2013:176. SCIE (IF- 0.966) https://doi.org/10.1186/1029-242X-2013-176  P17
  9. S. Sivaprasad Kumar, Virendra Kumar, "Fekete-Szego Problem for a Class of Analytic Functions defined by Convolution", Tamkang Journal of Mathematics, Vol. 44, No. 2, 2013. ESCI, SCOPUS https://doi.org/10.5556/j.tkjm.44.2013.1162 P16
  10. S. Sivaprasad Kumar, Virendra Kumar, “Fekete-Szego Problem for a Class of Analytic Functions”, Studia Universitatis Babeº-Bolyai Mathematica journal, 8(2013), No. 2, 181–188. ESCI, SCOPUS  P15
  11. S. Sivaprasad Kumar, Virendra Kumar, V. Ravichandran, “Subordination and superordination for multivalent functions defined by linear operator”, Tamsui Oxford J. of Inform. and Math. Sci. 29(3) (2013) 361-387.  P14
  12. S. Sivaprasad Kumar and Virendra Kumar, Some Sandwich Results Associated With a Generalized Linear Operator, ROMAIJ., v.9, no.2(2013), 107–118  P13
  13. Rosihan M. Ali, NakEun Cho, S. Sivaprasad Kumar, and V. Ravichandran, “Differential subordinations for functions associated with the lemniscate of Bernoulli”, Taiwanese Journal of Mathematics, Vol. 16, No. 3, pp. 1017-1026,  2012. SCIE (IF-0.749) https://doi.org/10.11650/twjm/1500406676 P12
  14. V. Ravichandran, and S. Sivaprasad Kumar, “Argument estimate for starlike functions of reciprocal order”, The Southeast Asian Bulletin of Mathematics, (2011) 35: 837-843.   P11
  15. S. Sivaprasad Kumar and H. C. Taneja, “On a class of meromorphic functions defined by certain linear operators”, Kyungpook Math. J. 49 (2009), no. 4, 631-646. SCOPUS https://doi.org/10.5666/KMJ.2009.49.4.631  P10
  16. S. Sivaprasad Kumar, V. Ravichandran, H. C. Taneja, “Differential sandwich theorems for linear operators”, International Journal of Mathematical Modeling, Simulation and Applications, Vol. 2 No. 4 (2009), pp. 490-507.  P9
  17. S. Sivaprasad Kumar, H. C. Taneja and V. Ravichandran, “Classes of multivalent functions defined by Dziok-Srivastava linear operator and multiplier transformation”, Kyungpook Mathematics Journal, Vol. 46, No. 1 (2006), 97-109. SCOPUS P8
  18. V. Ravichandran and S. Sivaprasad Kumar, “On sufficient conditions for starlikeness”, South East Asian Bulletin of Mathematics, Vol. 29 (2005), 773-783.   https://doi.org/10.1155/S0161171202007895 P7
  19. S. Sivaprasad Kumar, V. Ravichandran, and G. Murugusundaramoorthy, “Classes of meromorphic p-valent functions with positive coefficients”, Australian Journal of Mathematical Analysis, Vol. 2 No 2. (2005) Article No. 3. MR2161434 SCOPUS P6
  20. V. Ravichandran and S. Sivaprasad Kumar, H. C. Taneja, “Meromorphic functions with positive coefficients defined using convolution”, Journal of Inequalities in Pure and Applied Mathematics, Vol. 6 No. 2, Article 58 (2005). MR2150912, Zbl pre02218575  P5
  21. V. Ravichandran and S. Sivaprasad Kumar, “On a class of analytic functions involving Carlson-Shaffer linear operator”, Rivista di Mathematika Univ. Parma, Vol. 7, No. 3, (2004), pp. 35-48. MR2130409 (2005m:30016), Zbl pre02162695 SCOPUS P4
  22. V. Ravichandran, S. Sivaprasad Kumar and K. G. Subramanian, “Convolution conditions for spirallikenes and convex spirallikeness of certain meromorphic $p$-valent functions”, Journal of Inequalities in Pure and Applied Mathematics, 5 (1) (2004), Article No. 11. MR2048487 (2004m:30023), Zbl 1062.30017  P3
  23. V. Ravichandran, Herb Silverman, S Sivaprasad Kumar and K. G. Subramanian, “On Differential Subordination for a class of analytic functions defined by a linear operator”, International Journal of Mathematics and Mathematical Sciences, Vol. 2004 No. 42 (2004), pp. 2219-2230. MR2100102 (2005h:30050), Zbl pre02171586 SCOPUS  https://doi.org/10.1155/S0161171204309208  P2
  24. V. Ravichandran, S. Sivaprasad Kumar, Maslina Darus, “On a subordination theorem for a class of meromorphic functions, Journal of Inequalities in Pure and Applied Mathematics”, 5 (1) (2004), Article No.8. MR2048484, Zbl 1049.30015.  P1

Papers in Conference Proceedings

  1. Mundalia M., S. Sivaprasad Kumar (2020) Coefficient Bounds for a Unified Class of Holomorphic Functions. In: Deo N., Gupta V., Acu A., Agrawal P. (eds) Mathematical Analysis I: Approximation Theory. ICRAPAM 2018. Springer Proceedings in Mathematics & Statistics, vol 306. Springer, Singapore. https://doi.org/10.1007/978-981-15-1153-0_17  C6
  2. K. Khatter, V. Ravichandran and S. Sivaprasad Kumar, Estimates for initial coefficients of certain starlike functions with respect to symmetric points, in {it Applied analysis in biological and physical sciences}, 385--395, Springer Proc. Math. Stat., 186, Springer, New Delhi.   https://doi.org/10.1007/978-81-322-3640-5_2  C5
  3. Kanika Khatter, V. Ravichandran, and S. Sivaprasad Kumar, “Janowski Starlikeness and Convexity”, Proceedings of the Jangjeon Mathematical Society, 2017. SCOPUS  C4
  4. S. Sivaprasad Kumar, Virendra Kumar, On the Feketo-Sezgo inequality for a class of Analytic functions defined by Convolution, Proceedings of the International Conference on CMCGS-2012, held in Singapore during 30-31 January 2012. C3
  5. S. Sivaprasad Kumar, Virendra Kumar, On Feketo-Sezgo Problem for some subclasses of Analytic functions defined by Hadamard Product, Proceedings of    International Conference on Mathematical Science and Applications, held on 18th December 2011. C2
  6. V. Ravichandran, S. Sivaprasad Kumar and R. Usha, “Meromorphic starlike functions with positive coefficients associated with parabolic regions”, Proceedings of the Symposium on Geometric Function Theory -- 2002, Chennai, 2002, pp. 33--40.  C1

 

Invited Talks

  1.  "Strategies for Effective Research Article Writing",  was held on 8th November 2024, Organized by the Department of Mathematics and Astronomy, University of Lucknow.

  2. "Mastering the Art of Research Article Writing”,  was held on 20th August 2024, (FIP-6), organized by (CPDHE), UGC (MMTTC), University of Delhi.

  3. "Counterexamples in Real Analysis" was held on 25 April 2024 at the Department of Mathematics, Indraprastha College, DU, Delhi.

  4. "LATEX IN ICT Integrated Research in Mathematical Sciences” held on 24-30 September 2018 at Ramanujan College, University of Delhi.
  5. "MATLAB in National workshop on MATLAB and LATEX” held 24-30 August 2016 at  Dept. of Mathematics, Indira Gandhi University, Rewari.

Administrative Contributions:

  • Served as Head of the Department(2021-2023), securing AICTE approval for the B.Tech. (MC) program and achieving NBA accreditation (2023).
  • Facilitated the procurement of 25 high-configuration computers for the department laboratory (2023).

Research Project:

Completed a DTU-funded project (2023).

          Title:  “Coefficient Estimates and Differential Subordinations for Certain Class of Analytic Functions” under a faculty research project grant of DTU was done during 2019-23.

Papers presented at Conferences

  1. Participated and presented the paper entitled “Starlikeness criteria for certain analytic functions”, in the International Conference of the Indian Mathematics Consortium (ICTIMC), held during 14 – 17 December, 2016 at Banaras Hindu University, Varanasi, Uttar Pradesh, India.
  2. Participated and presented the paper entitled “Radius of Starlikeness for certain analytic functions”, in the National Conference on Emerging Trends in Mathematics and Mathematical Sciences (NCETMMS-2015), organized by Calcutta Mathematical Society, held at Kolkata during 17-19, Dec 2015
  3. Participated and presented a paper entitled "On Radius Problems for Sine-Starlike Functions" 23rd International Conference of Forum for Interdisciplinary Mathematics, Statistical & Computational Techniques (IMSCT-2014- FIM XXIII), Department of Mathematical and Computational Sciences, NIT(Karnataka), Surathkal, Karnataka, during 18-20 December, 2014.
  4. Participated and presented a paper entitled "Initial Coefficient Estimates for Bi-univalent functions" in the International conference on 'Special Functions and their Applications ICSFA-2013', organized by the Mathematics & Mechanical Engineering departments of MNIT,Jaipur  during 13-15 December, 2013.
  5. Participated and presented a paper entitled "On the Fekete-Szego inequality for a class of analytic functions defined by convolution" in the International conference on Computational Mathematics, Computational Geometry & Statistics-2012 (CMCGS-2012), held at Singapore during January 30,31 2012
  6. Presented a paper entitled "Fekete-Szego problem for some subclasses of analytic functions defined by Hadamard product" in the 1st International Conference on Mathematical Scinences and Applications held at Inda International center, New Delhi on 18-12-2011.
  7. Presented a paper entitled "Estimate for the inital coefficients of Biunivalent functions" in the National conference on Mathematical Modeling and Computer Simulation" held at IT-BHU, Varanasi on during 29-25 Mar 2012.
  8. Participated and presented the paper entitled “On a class of Meromorphic functions defined by certain linear operators” in the International conference on Geometric Function Theory and special functions and applications during January 02-05, 2006.
  9. Participated and presented the paper entitled “On the class of uniformly α-close to convex functions” in the International conference on Geometric Function Theory and special functions and applications during January 02-05, 2006.

Joint Papers presented by my Research Scholars:

  1. Presented (by Priyanka) the paper entitled “Inverse coefficient bounds of close to convex functions involving functions with integer coefficients”, in the International Conference on Mathematical Analysis and its Applications held during 14-16 December, 2019 at South Asian University, Delhi, India.
  2. Presented (by Shagun) the paper entitled “The sharp bound of the Hankel determinant H2(3) for the class SL*”, in the International Conference on Mathematical Analysis and its Applications held during 14-16 December, 2019 at South Asian University, Delhi, India.
  3. Presented (by Shagun) the paper entitled “On bounds of the Hankel determinants involving lemniscate of Bernoulli”, in the National conference on Advances in Mathematical Analysis and its Applications held during 08-10 Nov, 2019 at PGDAV College, Delhi, India.
  4. Presented (by Priyanka) the paper entitled “On Sharp coefficient estimates for Certain close to convex functions”, in the National conference on Advances in Mathematical Analysis and its Applications held during 08-10 Nov, 2019 at PGDAV College, Delhi, India.
  5. Presented (Mridula) the paper entitled “On inclusion relations of strongly starlike functions”, in the National conference on Advances in Mathematical Analysis and its Applications held during 08-10 Nov, 2019 at PGDAV College, Delhi, India.
  6. Presented (by Kamaljeet) the paper entitled “A general majorization result for some classes of starlike functions”, in the National conference on Advances in Mathematical Analysis and its Applications held during 08-10 Nov, 2019 at PGDAV College, Delhi, India.
  7. Presented (by Pooja) the paper entitled “A note on Janowski function”, in the National conference on Advances in Mathematical Analysis and its Applications held during 08-10 Nov, 2019 at PGDAV College, Delhi, India.
  8. Presented (by Priyanka) the paper entitled “Differential subordinations for starlike functions associated with modified sigmoid function”, in the 22nd Ramanujan Symposium National Conference on pure and applied Mathematics held during 06-08 March, 2019 at University of Madras, Chennai, India.
  9. Presented (by Shagun) the paper entitled “Strongly starlikeness criteria involving certain differential subordinations”, in the 22nd Ramanujan Symposium National Conference on pure and applied Mathematics held during 06-08 March, 2019 at University of Madras, Chennai, India.
  10. Presented (by Kamaljeet) the paper entitled “Coefficient Estimates for certain subclasses of strongly starlike functions”, in the National Conference on Mathematical Analysis and Computing held during 13-14 December, 2018 at SSN College of Engineering, Chennai, India.
  11. Presented (by Priyanka) the paper entitled “Certain class of starlike functions associated with Modified Sigmoid function”, in the International conference on recent advances in pure and applied mathematics held during 23-25 October, 2018 at Delhi Technological University, India.
  12. Presented (by Shagun) the paper entitled “Strongly Starlikeness Criteria for certain Analytic functions”, in the International conference on recent advances in pure and applied mathematics held during 23-25 October, 2018 at Delhi Technological University, India.
  13. Presented (by Kamaljeet) the paper entitled “Coefficient estimates for certain subclass of strongly starlike functions”, in the International conference on recent advances in pure and applied mathematics held during 23-25 October, 2018 at Delhi Technological University, India.
  14. Presented (by Mridula) the paper entitled “Coefficient estimates for a class of analytic functions”, in the International conference on recent advances in pure and applied mathematics held during 23-25 October, 2018 at Delhi Technological University, India.
  15. Presented (by Kush) the paper entitled “On a subclass of strongly starlike functions associated with cardioid domain”, at the International conference on recent advances in pure and applied mathematics held during 23-25 October 2018 at Delhi Technological University, India.
  16. Presented (by Mridula) the paper entitled “Coefficient estimates for a unified class of analytic functions”, at the 33rd Annual Conference of the Ramanujan Mathematical Society held during 1-3 June 2018 at the University of Delhi, India.

Association with Professional Societies:

·         Life Member of Research Group in Mathematical Inequalities and Applications (RGMIA)

·         Life Member of the Indian Mathematical Society

·         Life Member of the Society for special functions and its applications

 

Last Updated : 2025-08-29 16:30:54