Applied Mathematics
Phone:+91-11-27852217
Email: naokantdeo@dce.ac.in
Qualifications
M. Sc.(Mathematics), Ph. D.(Approximation Theory)
Areas of Interest
Approximation Theory and Real Analysis
Honours and Awards
CAS-TWAS Postdoctoral Fellowship-2005, (Chinese Academy of Sciences, Beijing, China and International Centre for Theoretical Physics, Trieste, Italy).
SCHOLARLY ACTIVITIES
- Expert of Union Public Service Commission (UPSC).
- External Expert from Academia of Board of Studies (BoS) in Mathematics under the faculty of Scientific Skills, Delhi Skill and Entrepreneurship University (DSEU), Delhi, w.e.f. 31st May 2024.
- Member of the Special Committee of the School of Physical Sciences, Jawaharlal Nehru University, New Delhi, w.e.f. January 2021.
- Honorary Professor, Department of Distance & Continuing Education at the University of Delhi, Delhi, w.e.f. March 2022.
- Member of Board of Studies, Department of Mathematics, Gautam Buddha University, UP, 2022-2023.
- Member of the board of studies (BOS), Department of Mathematics, Jaypee Institute of Information Technology (JIIT), Noida, UP, w.e.f. November 2023.
- Member of Governing Body (University Representative), Shaheed Rajguru College of Applied Sciences for Women, University of Delhi, 2022-23.
- Member of Governing Body (University Representative), Kamala Nehru College, University of Delhi, 2020-2021.
- Member of the board of studies (BOS) of Rungta Engineering College & Technology, Bhilai, Chhattisgarh, w.e.f. February 2023.
Ph. D. THESES SUPERVISED/UNDER SUPERVISION:
Ph. D. awarded (Individually) by DTU, Delhi:
- Neha Bhartdvaj: Some problems in approximation for certain discrete and integral operators.
- Minakshi Dhamija: Convergence Estimates for Certain Linear Positive Operators.
- Ram Pratap: Certain Approximation Methods of Convergence for Linear Positive Operators.
- Navshakti Mishra: A study on estimates of Convergence of Certain Approximation Operators.
- Chandra Prakash: Analysis of Certain Approximation Operators.
- Lipi: Approximation of Functions by Certain Positive Linear Methods of Convergence.
- Neha: Study on Some Generalised Approximation Operators.
Ph. D. registered in DTU, Delhi:
- Sandeep Kumar: Convergence analysis of some Approximation Operators.
- Kanita: A study on the approximation order of positive linear operators by certain approximation methods.
- Kapil: Study on Convergence of Certain Approximation Operators.
- Mahima: Approximation of operators by certain Approximation Methods.
ADMINISTRATIVE EXPERIENCE
- Head of Department of B.Tech. (B. Tech. Programme Under Continuing Education) , DTU, 2018 - 2022
- Member of the board of studies (BOS) of Rungta Engineering College $&$ Technology, Bhilai, Chhattisgarh, w.e.f. February $2023$.
- Chairman B.Tech.(Evening), Admission Examination 2018, 2019, 2020, 2021, 2022
- Dy. Controller of Examination, DTU, 2013-2017
- Hostel Warden 2003-2006
Membership in Academic Bodies/Societies
- Life member of the Indian Mathematical Society (IMS), INDIA.
- Member of Research Group in Mathematical Inequalities and Applications (RGMIA), Melbourne, AUSTRALIA.
- A regular World Academy of Young Scientists (WAYS) member, Budapest, HUNGARY.
Reviewer:
- Member of reviewer’s panel of American Mathematical Society (AMS).
- Member of reviewer’s panel of Zentralblatt MATH.
- Various International and National Journals.
Conference and Course Organized:
- International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), 23-25 October 2018.
- AICTE sponsored a staff development programme on Soft Computing using Matlab and LaTeX at a Glance, 7-18 December 2009.
Associated with Professional Societies:
- Member of Research Group in Mathematical Inequalities and Applications (RGMIA), Melbourne, Australia.
- A regular World Academy of Young Scientists (WAYS) member, Budapest, Hungary.
- Life member of the Indian Mathematical Society (IMS), India.
Invited Speaker/Keynote Speaker/Chairperson:
- Speaker: 1st International Conference on ``Role of Applied Science in Social Implications (IC-RASSI)", Certain Positive Linear Operators and Approximation Methods, Govt. Digvijay Autonomous P.G. College Rajnandgaon, Chhattisgarh, India, $6-8$ February $2023$.
- Speaker: Convergence Estimates - an overview, Refresher Course on ``Non-linear Analysis for the Development of Neural Network System" Department of Mathematics, G. G. University, Bilaspur, Chhattisgarh, 24th September 2021.
- Speaker: Direct Estimates in Approximation, Refresher Course in Applied Mathematics, Ranchi University, Ranchi, Jharkhand, 23rd September 2021.
- Keynote Speaker: Integral Modification of Positive Linear Operators, International Conference on ''Mathematical Modeling and High-Performance Computing in Science and Technology”, RGPV, Bhopal (M. P), February 12 - 13, 2020.
- Speaker: A Generalisations of Positive Linear Operators and Its Variants, ''International Conference on Mathematical Analysis and its Application (ICMAA-2019)”, Department of Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi, India, December 14 - 16, 2019.
- Speaker: Approximation Operators and their Variants, ''Workshop on Recent Trends in Physical Sciences & its Applications”, Department of Mathematics, Dr Bhimrao Ambedkar University, Agra, November 7-8, 2019.
- Chair Person: "International Conference on Recent Advances in Pure and Applied Mathematics", Delhi Technological University, Delhi, October 23-25, 2018.
- Speaker: "International Conference of CONIAPS-XIV", Sardar Vallabhbhai National Institute of Technology, Surat, December 22-24, 2011.
- Speaker/Chair Person: "Some problems related to linear positive operators, NCKMS-2009", National Conference on Establishing Kinship between Mathematical Sciences & Society, Durg, Chhattisgarh, October 30-31, 2009.
Books Published :
- ''Introduction to Mathematical Analysis'', Authors: Naokant Deo, Ryozi Sakai, Springer-Verlag, Softcover ISBN: 978-981-15-1159-2.
- "Mathematical Analysis I – Approximation Theory'', ICRAPAM 2018, New Delhi, India, October 23-25, Editors: Deo, Naokant, Gupta, V., Acu, A.M., Agrawal, P.N.(Eds.), Springer-Verlag, Print ISBN 978-981-15-1152-3; Electronic ISBN 978-981-15-1153-0.
- "Mathematical Analysis II – Optimisation, Differential Equations, and Graph Theory'', ICRAPAM 2018, New Delhi, India, October 23-25, Editors: Deo, Naokant, Gupta, V., Acu, A.M., Agrawal, P.N.(Eds.), Springer-Verlag Print ISBN: 978-981-15-1156-1; Electronic ISBN: 978-981-15-1157-8.
Recent Publications:
- M. Tomar and Naokant Deo, ``Theoretical validation and comparative analysis of higher-order modified Bernstein operators", Iran. J. Sci., (2024), SCIE, I.F. 1.7 (Accepted).
- Kanita and Naokant Deo, ''Parametric Bernstein operators based on contagion distribution” Math. Methods Appl. Sci., (2024), SCIE, I.F. 3.007 (Accepted).
- Sandeep Kumar and Naokant Deo, ''Convergence analysis of semi-exponential Post-Widder operators", Miskolc Math. Notes, (2024), SCIE, I.F. 1.085, Accepted.
- Neha and Naokant Deo, ''Generalization of parametric Baskakov operators based on the I-P-E distribution", FILOMAT, SCIE (2023), Accepted.
- Neha and Naokant Deo, ''An approach to preserve functions with exponential growth by using modified Lupac{s}-Kantrovich operators", Numer. Funct. Anal. Optim., (2023), SCIE, I.F. 1.41, url{https://doi.org/10.1080/01630563.2023.2263977}
- Neha and Naokant Deo, "Iterative combinations of generalised operators", Matematicki Vesnik, ESCI (2023), Accepted.
- Naokant Deo and Km. Lipi, ''Approximation by means of modified Bernstein operators with shifted knots,'' The Journal of Analysis, SCOPUS (2023) Accepted.
- Km. Lipi and Naokant Deo, "$lambda$-Bernstein operators based on Polya distribution", Numer. Funct. Anal. Optim., SCIE, 44(6)(2023), 529-544, https://doi.org/10.1080/01630563.2023.2185896.
- Neha, and Naokant Deo "Integral modification of Beta-Apostol-Genocchi operators'', Math. Found. Comp., ESCI, (2022), Doi: 10.3934/mfc.2022039
- Chandra Prakash, D. K. Verma and Naokant Deo, "Approximation by Durrmeyer variant of Cheney-Sharma Cholodovsky Operators", Math. Found. Comp., ESCI, (2022), Doi: 10.3934/mfc.2022034
- Naokant Deo, Chandra Prakash, D. K. Verma, "Approximation by Apostol-Genocchi summation-integral type operators", Miskolc Math. Notes, SCIE, (2022), in press.
- Nav Shakti Mishra and Naokant Deo, "Approximation by generalized Baskakov Kantorovich operators of arbitrary order", Bull. Iranian Math. Soc., SCIE, Springer-Verlag, 48(2022), 3839–3854.
- Km. Lipi and Naokant Deo, "Approximation properties of modified Gamma operators preserving t^{v}", Annals of Functional Analysis, SCIE, Birkhäuser (2022), https://doi.org/10.1007/s43034-022-00172-x.
- Nav Shakti Mishra and Naokant Deo, "Convergence Estimates of certain Gamma type operators'', Math. Methods Appl. Sci., SCIE, Wiley, (2021), in press.
- Nurhayat Ispir, Naokant Deo, and Neha Bhardwaj "Approximation of Jain operators by statistical convergence'', Thai J. Math., ESCI, 19(4) (2021),
- Neha, Ram Pratap, and Naokant Deo, "Bezier variant of summation-integral type operators" Rend. Circ. Mat. Palermo, II. Ser (2022), ESCI, Springer-Verlag, https://doi.org/10.1007/s12215-021-00695-7.
- Minakshi Dhamija, Naokant Deo, Ram Pratap, Ana Maria Acu, "Generalized Durrmeyer operators based on inverse Polya-Eggenberger distribution'', Afr. Mat., ESCI, Springer-Verlag, (2021), in press.
- Chandra Prakash, D.K. Verma, and Naokant Deo "Approximation by a new sequence of operators involving Apostol-Genocchi polynomials", Math. Slovaca, SCIE, De Gruyter, 71 (2021), No. 5, 1179-1188.
- Nav Shakti Mishra and Naokant Deo, "Approximation by a composition of Apostol-Genocchi and Paltanea-Durrmeyer operator", ESCI, Kragujevac J. Math, 48(4) (2024), 629-646.
- Neha and Naokant Deo, "Integral modification of Apostol-Genocchi operators", SCIE, Filomat 35:5 (2021), 1465–1475.
- Sandeep Kumar and Naokant Deo, "Approximation of generalized Paltanea and Heilmann-type operators", Matematicki Vesnik, ESCI, 74(2)(2022), 101-109.
- Km. Lipi and Naokant Deo, "On modification of certain exponential type operators preserving constant and $e^{-x}$", Bull. Malays. Math. Sci. Soc., SCIE, Springer-Verlag, (2021), in press.
- Nav Shakti Mishra and Naokant Deo, "On the preservation of functions with exponential growth by modified Ismail-May operators'', Math. Methods Appl. Sci., SCIE, Wiley, (2021), in press.
- Ram Pratap and Naokant Deo, "A family of Bernstein-Kantorovich operators with shifted knots", Rendiconti del Circolo Matematico di Palermo Series 2, ESCI, Springer-Verlag, (2021), doi.org/10.1007/s12215-021-00677-9
- Naokant Deo and Ram Pratap, "The family of Sz'asz-Durrmeyer type operators Involving Charlier Polynomials", ESCI, Kragujevac J. Math, 47(3)(2023), 431-443.
- Naokant Deo and Sandeep Kumar, "Durrmeyer Variant of Apostol-Genocchi-Baskakov Operators", Quaest. Math. SCIE, Taylor & Francis, (2020), doi.org/10.2989/16073606.2020.1834000.
- Neha and Naokant Deo, "Convergence and Difference Estimates Between Mastroianni and Gupta Operators", ESCI, Kragujevac J. Math, 47(2)(2023), 259-269.
- Nav Shakti Mishra and Naokant Deo, "Kantorovich Variant of Ismail-May Operators", Iran. J. Sci. Technol. Trans. A Sci., SCIE, Springer-Verlag, (2020), doi.org/10.1007/s40995-020-00863-x
- Km. Lipi and Naokant Deo, "General family of exponential operators", SCIE, Filomat, Vol 34, No 12 (2020)
- Naokant Deo and Ram Pratap, "Approximation by Mixed Positive Linear Operators based on Second-Kind Beta Transform", Asian-Eur. J. Math., SCIE, World Scientific (2020), In-press.
- Ram Pratap and Naokant Deo, "α-Bernstein-Kantorovich operators", Afr. Mat., ESCI, Springer-Verlag, 31 (2020), 609-618.
- Naokant Deo and Ram Pratap, "Approximation by integral form of Jain and Pethe operators", Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, SCIE, Springer-Verlag, (2020), doi.org/10.1007/s40010-020-00691-z
- Ram Pratap and Naokant Deo, "q-Analogue of generalized Bernstein-Kantorovich operators", Mathematical Analysis-I, Approximation Theory, ICRAPAM - 2018, New Delhi, India, October 23-25, Springer-Verlag, Scopus (2020), 67-75.
- Naokant Deo, Minakshi Dhamij and Dan Miclaus, "New Modified Baskakov Operators Based On The Inverse Polya-Eggenberger Distribution", SCIE, Filomat, 33:11 (2019), 3537–3550.
- Ram Pratap and Naokant Deo, "Rate of convergence of Gupta-Srivastava operators based on certain parameters", J. Class. Anal., 14(2) (2019), 137-153.
- Ram Pratap and Naokant Deo, "Approximation by genuine Gupta–Srivastava operators", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, Springer-Verlag , Scopus, 113(2019), 2495-2505.
- Naokant Deo and Minakshi Dhamija, “Generalized positive linear operators based on PED and IPED”, Iran. J. Sci. Technol. Trans. A Sci., SCIE, Springer-Verlag, (2018), 1-7.
- Minakshi Dhamija, Ram Pratap and Naokant Deo, “Approximation by Kantorovich form of modified Szasz-Mirakyan operators”, Appl. Math. Comput., SCI, Elsevier 317 (2018), 109-120.
- Minakshi Dhamija and Naokant Deo “Approximation by generalized positive linear-Kantorovich operators”, SCIE, Filomat, 31:14 (2017), 4353-4368.
- Naokant Deo and Minakshi Dhamija, “Charlier-Szasz-Durrmeyer type positive linear operators, Afr. Mat., ESCI, Springer-Verlag. DOI 10.1007/s13370-017-0537-1, (2017).
- Naokant Deo and Minakshi Dhamija, “Better approximation results by Bernstein-Kantorovich operators”, Lobache vskii J. Math., SCIE, Springer-Verlag., Vol. 38(1)(2017), 94-100.
- Naokant Deo and Neha Bhardwaj, “Quantitative estimates for generalized two-dimensional Baskakov operators”, Korean J. Math., ESCI, 24(3) (2016), 335-344.
- Naokant Deo and Neha Bhardwaj, Direct and Inverse Theorems for Beta-Durrmeyer Operators, Modern Mathematical Methods and High-Performance Computing in Science and Technology, series Springer Proceedings in Mathematics & Statistics Vol. 171(2016), 179-191 Springer-Verlag.
- Minakshi Dhamija and Naokant Deo, Jain-Durrmeyer operators associated with the inverse Polya-Eggenberger distribution”, Appl. Math. Comput. SCI, Elsevier, Vol. 286 (2016), 15-22.
- Naokant Deo, Minakshi Dhamija and Dan Miclaus, “Stancu-Kantorovich operators based on inverse Polya-Eggenberger distribution”, Appl. Math. Comput. SCIE, Elsevier, Vol. 273(1) (2016), 281-289.
- Minakshi Dhamija, Ryozi Sakai and Naokant Deo, “On approximation by Phillips type modified Bernstein operator in a mobile interval”, J. Class. Anal., Vol. 7(1)(2015), 25-37.
- Naokant Deo and Neha Bhardwaj, “A better error estimation on Balazs operators”, Lobache Vskii J. Math. SCIE, Springer-Verlag., Vol. 36(1)(2015), 9-14.
- Naokant Deo, Mehmet Ali Ozarslan, and Neha Bhardwaj, “Statistical convergence for general Beta operators”, Korean J. Math., 22(2014), No. 4, 671-681.
- H. S. Jung, Naokant Deo and Minakshi Dhamija, “Pointwise approximation by Bernstein type operators in mobile interval”, Appl. Math. Comput., SCI, Elsevier, Vol. 214(1) (2014), 683-694.
- Dan Barbosu and Naokant Deo, “Some Bernstein-Kantorovich operators”, Automation Computers Applied Mathematics, SCIE Vol. 22(1) (2013), 15-21.
- Naokant Deo, H. S. Jung and R. Sakai, “Degree of approximation by hybrid operators”, Abstract and Applied Analysis, SCIE, Vol. (2013), Article ID 732069, 8 pages.
- Naokant Deo, Neha Bhardwaj and S. P. Singh, “Simultaneous approximation on generalized Bernstein-Durrmeyer operators”, Afr. Mat., ESCI, Springer-Verlag, Vol. 24(1) (2013), 77-82.
- V. Gupta, Naokant Deo and Xiao-Ming Zeng, “Simultaneous approximation for Szasz-Mirakian-Stancu-Durrmeyer operators”, Anal. Theory Appl., Vol. 29(1) (2013), 86-96.
- Naokant Deo and Neha Bhardwaj, “A better error estimation on Szasz-Baskakov-Durrmeyer operators”, Springer-Verlag, Scopus, Proceedings in Mathematics & Statistics, [Chapter 21], Advances in Applied Mathematics and Approximation Theory, Vol. XIX(2013), 329-337.
- Naokant Deo, "Faster rate of convergence on Srivastava-Gupta operators", Appl. Math. Comput. SCI, Elsevier, Vol. 218(21) (2012), 10486-10491.
- P. Verma, S. P. Singh, A. S. Randive and Naokant Deo, "On the Degree of $L_1$-Approximation by Meyer-Konig Zeller operators" SEA. Bull. Math., Vol. 35 (2011), 523-528.
- V. Gupta and Naokant Deo, "A note on improved estimations for integrated Szasz-Mirakyan operators", Math. Slovaca, SCIE, De Gruyter, Vol. 61(5) (2011), 799-806.
- V. Gupta and Naokant Deo, "A Note on rate of approximation for certain Bezier-Durrmeyer operators, Mat. Vesnik., ESCI, Vol. 63(1) (2011), 27-32.
- Naokant Deo and Neha Bhardwaj, "On the degree of approximation by modified Baskakov operators", Lobachevskii J. Math., Springer-Verlag, SCIE, Vol. 32(1) (2011), 16-22.
- Naokant Deo and Neha Bhardwaj, "Some approximation results for Durrmeyer operators", Appl. Math. Comput. SCIE, Elsevier, 217(12) (2011), 5531-5536.
- Naokant Deo and Neha Bhardwaj, "Some approximation theorems for multivariate Bernstein operators", SEA. Bull. Math., Vol. 34 (2010), 1023-1034.
- Naokant Deo, "On the degree of approximation for bivariate Lupacs type operators", J. Appl. Math. Inform., Vol. 28, No. 5-6 (2010), 1101-1116.
- Naokant Deo and S. P. Singh, "On the degree of approximation by new Durrmeyer type operators", General Math., Vol. 18, No. 2 (2010), 195-209.
- Naokant Deo, "Pointwise estimate for modified Baskakov type operator}, Lobachevskii J. Math., Vol. 31, No. 1 (2010), 36-42, Springer-Verlag., SCIE
- Naokant Deo, "Direct result on exponential-type operators" Appl. Math. Comput. SCI, Elsevier, 204 (2008), 109-115.
- Naokant Deo, M. A. Noor and M. A. Siddiqui, "On approximation by a class of new Bernstein type operators", Appl. Math. Comput. SCI, Elsevier, 201 (2008), 604-612.
- Naokant Deo, "Direct result on the Durrmeyer variant of Beta operators", SEA. Bull. Math., Vol. 32 (2008), 283-290.
- Naokant Deo and D. Yan. "Simultaneous approximation on Szasz-Mirakian-Baskakov type operators", Acta Math. Sinica, Vol. 50, No. 6 (2007), 1257-1262.
- Naokant Deo, "On the iterative combinations of Baskakov operator", General Math., Vol. 15, No. 1 (2007), 51-58.
- Naokant Deo, "Equivalent theorem on Lupacs operator", J. Inequal. Pure and Appl. Math., Vol. 8, Issue 4, (2007), 1-9.
- Naokant Deo, "Voronovskaya type asymptotic formula for Lupacs-Durrmeyer operators", Rev. Un. Mat. Argentina., SCIE, Vol. 48, No. 1 (2007), 47-54.
- Naokant Deo, "A note on equivalence theorem for Beta operators", Mediterr. J. Math. SCIE, Springer-Verlag, Vol. 4, No. 2, (2007), 245-250.
- Naokant Deo, "Quantitative estimate of approximation by exponential-type operators", SEA. Bull. Math., Vol.31, (2007), 465-470.
- Naokant Deo, "Simultaneous approximation by two-dimensional hybrid positive linear operators" General Math., Vol. 14, No. 4 (2006), 15-28.
- Naokant Deo, "Simultaneous approximation by two-dimensional Lupac{s}-Durrmeyer operators", J. of Math. Anal. and Approximation Theory, Vol. 1, No. 2, (2006), 180-188.
- Naokant Deo, "Direct and inverse theorems for Sz'{a}sz-Lupac{s} type operators in simultaneous approximation", Mat. Vesnik., Vol. 58, No.1-2, (2006), 19-29.
- V. Gupta and Naokant Deo, "On the rate of convergence for bivariate Beta operators, General Math., Vol. 13, No. 3 (2005), 107-114.
- Naokant Deo "Simultaneous approximation for the linear combinations of modified Beta operators, Austral. J. of Math. Anal. and Appl., Vol. 2, No. 2, Art. 4, (2005), 1-12.
- Naokant Deo, "On the Rate of Convergence of modified Baskakov type operators on functions of bounded Variation", Kyungpook Math. J., ESCI, 45(2005), 71-77.
- Naokant Deo, "Simultaneous approximation by Lupacs modified operators with weighted function of Sz'{a}sz operators", J. Inequal. Pure and Appl. Math., 5(4) Art. 113, (2004), 1-5.
- Naokant Deo, "Lupas-Durrmeyer operators", J. Inequal. Pure and Appl. Math., 5(4) Art. 103, (2004), 1-5.
Conference Attended:
- 12th International Conference on Approximation Theory and its Applications", Lucian Blaga University of Sibiu, Romania, May 26-29, (2016).
- International Conference on Recent Advance in Mathematical Biology", Analysis and Applications, AMU, Aligarh, India, June 4-6, (2015).
- International Conference on Recent Trends in Mathematical Analysis and its Applications", IIT Roorkee in Roorkee, India, December 21-23, (2014).
- Faster Rate of Convergence on Modified Discrete and Integral Operators}, ``International Conference on Theory of Approximation of Functions and its Applications" Kamianets-Podilsky Ivan Ohienko National University, Kamianets-Podilsky, Ukraine, (2012).
- ICAA, International Conference on Analysis and Applications; Anhui, Hefei, CHINA, June 28- July 1, 2006.
- ICAHA, International Conference on Applicable Harmonic Analysis: Approximation and Computation; Beijing, CHINA, June 17-21, 2006.
- International Conference on Mathematical Inequalities and their Applications; I Victoria University, Melbourne, Victoria, AUSTRALIA, December 06 - 08, 2004.
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Researchgate: Naokant Deo (researchgate.net)
Last Updated : 2024-08-10 11:04:20