Professor Naokant Deo

Naokant Deo is a professor at the Department of Applied Mathematics, Delhi Technological University, New Delhi, India. He completed his Ph.D. in Mathematics from Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh, India. His areas of interest include real analysis and approximation theory with a focus on positive linear operators. Professor Deo is a recipient of the CAS-TWAS Fellowship awarded by the Chinese Academy of Sciences, Beijing, China, and the International Centre for Theoretical Physics, Trieste, Italy. He has published 92 papers in international and national journals. He is an active member of the Indian Mathematical Society, India, and the Research Group in Mathematical Inequalities and Applications, Australia. His research works have appeared in prestigious national and international journals.

Professor, Delhi Technological University

Honorary Professor, School of Open Learning, University of Delhi

34 years experience of teaching to undergraduate students

20 years experience of teaching to postgraduate students

1. Real Analysis
2. Lebesgue Integral
3. Engineering Mathematics
4. Numerical Analysis

1. Member of American Mathematical Society [AMS], USA
2. Member of the Research Group in Mathematical Inequalities and Applications [RGMIA], Melbourne, AUSTRALIA.
3. Regular member of World Academy of Young Scientists [WAYS], Budapest, HUNGARY.
4. Life member of Indian Mathematical Society (IMS)

• M. Tomar and Naokant Deo, ``Cardiovascular Disease Prediction using Machine Learning Algorithms with Bernstein-Type Kernel Functions",  J. Supercomput., 82(5), (2026),  \url{https://doi.org/10.1007/s11227-025-08128-3, SCIE, I.F. 2.7.

• Kanita and Naokant Deo, ''Analysis of semi-exponential Bernstein operators with Improved Order of Approximation", Math. Methods Appl. Sci., Accepted, SCIE, I.F. 3.007 (2025)

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  D. Khattar, Naokant Deo, and M. Sirohi ''Adaptive Multi-Switching Chaos Synchronization of Lotka–Volterra Model to Replicate Complete and Anti-Behavior of Hindmarsh–Rose Neuron Model", Bol. Soc. Port. Mat., ESCI, 44(7)(2026), 1-21, \url{http://dx.doi.org/10.5269/bspm.80743}.

• Kanita and Naokant Deo, ''Approximation of Linear Positive Fuzzy Operators", Bol. Soc. Port. Mat., \textbf{ESCI}, 44(7)(2026), 1-21, \url{http://dx.doi.org/10.5269/bspm.80942}.

• Naokant Deo, K. Kumar, and D. K. Verma, ''Better approximation and theoretical validation for integral-type operators", Matematicki Vesnik, ESCI, I.F. 0.8, Accepted, (2025).

   

• Naokant Deo, K. Kumar, and D. K. Verma, ''Better approximation and theoretical validation for integral-type operators", Matematicki Vesnik, ESCI, I.F. 0.8, Accepted, (2025).

• K. Kumar, Naokant Deo, and D. K. Verma, ''Parametric representation of integral operators for x > 0", Filomat, SCIE, I.F. 0.988, Accepted, (2025).

• Kanita and Naokant Deo, ''Bernstein type semi-exponential operators", Appl.Anal., SCIE, I.F. 1.1, Accepted, (2025).

• D. Khattar, Naokant Deo, and M. Sirohi ''On novel Hexa-compound combination synchronization over nineteen n-dimensional category-B chaotic systems and electronic circuit schematic", Phys. Scr., url{https://doi.org/10.1088/1402-4896/ad9e3c}, SCIE, I.F. 2.3, 100(2025) 015280.

• 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. Verm, 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
• 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”, Lobachevskii 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”, Lobachevskii 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, "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 the 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 Szasz-Lupas 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 Szasz 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.

Books:

1. ''Introduction to Mathematical Analysis'', Authors: Naokant Deo, Ryozi Sakai; Springer-Verlag, Softcover ISBN: 978-981-15-1159-2.
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.
3. "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

 

Book Chapters:

• Ram Pratap and Naokant Deo, "q-Analogue of generalised Bernstein-Kantorovich operators", Mathematical Analysis-I, Approximation Theory, ICRAPAM - 2018, New Delhi, India, October 23-25, Springer-Verlag, Scopus (2020), 67-75.
• 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.

CAS-TWAS Postdoctoral Fellowship-2005, (Chinese Academy of Sciences, Beijing, China and International Centre for Theoretical Physics, Trieste, Italy)