Dr. Durvesh Kumar Verma

@mirandahouse.ac.in

Assistant Professor, Department of Mathematics
Miranda House, University of Delhi

Dr. Durvesh Kumar Verma


                        Download Compact PDF  
https://researchid.co/dkverma

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematics
16

Scopus Publications

282

Scholar Citations

9

Scholar h-index

9

Scholar i10-index

Scopus Publications

  • Approximation by a new sequence of operators involving Laguerre polynomials
    Naokant Deo, Kapil Kumar, Kumar VermaDurvesh
    Filomat, 2025
    Thispaper presents a new integral approach for operators using the modified Laguerre polyno-mials and Păltă nea basis function to approximate functions over the interval [0, ∞). Further, the universal Korovkin’s theorem is established to investigate the approximation properties of the proposed opera-tors. Convergence analysis is examined through various analytical methods, including the Lipschitz class, Peetre’s K-functional, the second-order modulus of smoothness, and the modulus of continuity. The Voronovskaja-type asymptotic formula and approximation results in weighted spaces are also obtained. Finally, we employ Mathematica to present numerical examples that visually confirm the theoretical results.
  • Parametric representation of integral operators for x > 0
    Kapil Kumar, Naokant Deo, Durvesh Kumar Verma
    Filomat, 2025
    In the present paper, we introduce a new sequence of integral operators with a certain parameter ? that can be used to approximate the functions over the interval (0, ?) = R*. Firstly, we obtain the moments for the proposed operators. Next, we estimate some direct results, which include the rate of con-vergence, the asymptotic formula, and point-wise convergence in terms of modulus of continuity; weighted approximation for these operators is given, and some results related to the A-statistical convergence of the operators are obtained. Ultimately, in order to validate the ?ndings, we employ numerical illustrations and visual depictions.
  • APPROXIMATION BY DURRMEYER VARIANT OF CHENEY-SHARMA CHLODOVSKY OPERATORS
    Chandra Prakash, , Durvesh Kumar Verma, Naokant Deo, and
    Mathematical Foundations of Computing, 2023
    In this paper, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified and estimated the convergence properties using of modulus of continuity, Lipschitz- type space, and Ditzian-Totik modulus of continuity. After that, the weighted approximation result is also given. Finally, some results related to the A-statistical convergence of the operators are obtained.
  • APPROXIMATION BY APOSTOL-GENOCCHI SUMMATION-INTEGRAL TYPE OPERATORS
    Chandra Prakash, Naokant Deo, Durvesh Kumar Verma
    Miskolc Mathematical Notes, 2023
    . In the present paper, we proposed a new sequence of summation-integral type operators involving Apostol-Genocchi polynomials. We study some approximation results of the proposed operators using first and second-order modulus of continuity, the global rate of convergence using Voronovskaja-type asymptotic theorem, Lipschitz-type space, and Ditzian-Totik modulus of smoothness. Lastly, we study the weighted approximation.
  • Bézier variant of Bernstein-Durrmeyer blending-Type operators
    Chandra Prakash, Naokant Deo, D. K. Verma
    Asian European Journal of Mathematics, 2022
    In this paper, we construct the Bézier variant of the Bernstein–Durrmeyer-type operators. First, we estimated the moments for these operators. In the next section, we found the rate of approximation of operators [Formula: see text] using the Lipschitz-type function and in terms of Ditzian–Totik modulus of continuity. The rate of convergence for functions having derivatives of bounded variation is discussed. Finally, the graphical representation of the theoretical results and the effectiveness of the defined operators are given.
  • Approximation by a new sequence of operators involving Apostol-Genocchi polynomials
    Chandra Prakash, Durvesh Kumar Verma, Naokant Deo
    Mathematica Slovaca, 2021
    The main objective of this paper is to construct a new sequence of operators involving Apostol-Genocchi polynomials based on certain parameters. We investigate the rate of convergence of the operators given in this paper using second-order modulus of continuity and Voronovskaja type approximation theorem. Moreover, we find weighted approximation result of the given operators. Finally, we derive the Kantorovich variant of the given operators and discussed the approximation results.
  • Approximation by generalized Srivastava-Gupta operators based on certain parameter
    D.K. Verma
    Publications De L Institut Mathematique, 2017
    We establish some direct results in simultaneous approximation for a generalization of the Srivastava-Gupta operators. We establish pointwise convergence, Voronovskaja type asymptotic formula and an error estimate in terms of modulus of continuity of the function.
  • Approximation by a new sequence of operators involving charlier polynomials with a certain parameter
    D. K. Verma, Vijay Gupta
    Springer Proceedings in Mathematics and Statistics, 2016
  • Approximation for Jakimovski–Leviatan–Pǎltǎnea operators
    D. K. Verma, Vijay Gupta
    Annali Dell Universita Di Ferrara, 2015
  • A q-analogue of modified beta operators
    Vijay Gupta, P.N. Agrawal, Durvesh Kumar Verma
    Rocky Mountain Journal of Mathematics, 2013
    . In the present paper, we introduce a q - analogue of modified Beta operators. First we estimate moments of these operators and also obtain the relation for mo- ments. We estimate some approximation properties of these operators.
  • Approximation by Baskakov-Durrmeyer-Stancu operators based on q-integers
    D. K. Verma, P. N. Agrawal
    Lobachevskii Journal of Mathematics, 2013
  • Approximation by complex Favard-Szász-Mirakjan-Stancu operators in compact disks
    Vijay Gupta, Durvesh K Verma
    Mathematical Sciences, 2012
  • Convergence in simultaneous approximation for Srivastava-Gupta operators
    Durvesh Verma, Purshottam N Agrawal
    Mathematical Sciences, 2012
  • Approximation by complex Baskakov-Stancu operators in compact disks
    Sorin G. Gal, Vijay Gupta, D. K. Verma, P. N. Agrawal
    Rendiconti Del Circolo Matematico Di Palermo, 2012
  • Some approximation properties of Baskakov-Durrmeyer-Stancu operators
    D.K. Verma, Vijay Gupta, P.N. Agrawal
    Applied Mathematics and Computation, 2012
  • On discrete q-beta operators
    Vijay Gupta, P. N. Agrawal, Durvesh Kumar Verma
    Annali Dell Universita Di Ferrara, 2011

RECENT SCHOLAR PUBLICATIONS

  • Parametric representation of integral operators for x> 0
    K Kumar, N Deo, DK Verma
    Filomat 39 (14), 4791-4805 , 2025
    2025
  • Approximation by a new sequence of operators involving Laguerre polynomials
    N Deo, K Kumar, DK Verma
    Filomat 39 (34), 12345-12360 , 2025
    2025
    Citations: 1
  • Some Approximation Properties by Sz\'asz-P{\u{a}}lt{\u{a}}nea type Operators involving the Appell Polynomials of class
    N Deo, C Prakash, DK Verma
    arXiv preprint arXiv:2308.03304 , 2023
    2023
  • Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators.
    C Prakash, DK Verma, N Deo
    Math. Found. Comput. 6 (3), 535-545 , 2023
    2023
    Citations: 5
  • APPROXIMATION BY APOSTOL-GENOCCHI SUMMATION-INTEGRAL TYPE OPERATORS
    C Prakash, N Deo, DK Verma
    Miskolc Mathematical Notes 24 (1), 369-382 , 2023
    2023
    Citations: 2
  • Bézier variant of Bernstein–Durrmeyer blending-type operators
    C Prakash, N Deo, DK Verma
    Asian-European Journal of Mathematics 15 (06), 2250103 , 2022
    2022
    Citations: 4
  • Approximation by a new sequence of operators involving Apostol-Genocchi polynomials
    C Prakash, DK Verma, N Deo
    Mathematica Slovaca 71 (5), 1179-1188 , 2021
    2021
    Citations: 17
  • Approximation by generalized Srivastava-Gupta operators based on certain parameter
    DK Verma
    Publications de l'Institut Mathematique 101 (115), 247-259 , 2017
    2017
    Citations: 4
  • Approximation by a new sequence of operators involving Charlier polynomials with a certain parameter
    DK Verma, V Gupta
    Modern Mathematical Methods and High Performance Computing in Science and … , 2016
    2016
    Citations: 3
  • Polynomials with a Certain Parameter
    DK Verma, V Gupta
    Modern Mathematical Methods and High Performance Computing in Science and … , 2016
    2016
  • Approximation for Jakimovski–Leviatan–Pǎltǎnea operators
    DK Verma, V Gupta
    ANNALI DELL'UNIVERSITA'DI FERRARA 61 (2), 367-380 , 2015
    2015
    Citations: 18
  • Approximation by Baskakov-Durrmeyer-Stancu operators based on q -integers
    DK Verma, PN Agrawal
    Lobachevskii Journal of Mathematics 34 (2), 187-196 , 2013
    2013
    Citations: 11
  • Approximation for a new sequence of summation-integral type operators
    V Gupta, A Ravi P., DK Verma
    Advances in Mathematical Sciences and Applications 23 (1), 35-42 , 2013
    2013
    Citations: 21
  • A q-analogue of modified Beta operators
    V Gupta, PN Agrawal, DK Verma
    The Rocky Mountain Journal of Mathematics, 931-947 , 2013
    2013
    Citations: 4
  • Approximation by complex Favard-Szász-Mirakjan-Stancu operators in compact disks
    V Gupta, D K Verma
    Mathematical Sciences 6 (1), 25 , 2012
    2012
    Citations: 24
  • Convergence in simultaneous approximation for Srivastava-Gupta operators
    DK Verma, PN Agrawal
    Mathematical Sciences 6 (1), 22 , 2012
    2012
    Citations: 39
  • Simultaneous approximation by certain Baskakov–Durrmeyer–Stancu operators
    V Gupta, DK Verma, PN Agrawal
    Journal of the Egyptian Mathematical Society 20 (3), 183-187 , 2012
    2012
    Citations: 33
  • Approximation by complex Baskakov-Stancu operators in compact disks
    SG Gal, V Gupta, DK Verma, PN Agrawal
    Rendiconti del Circolo Matematico di Palermo 61 (2), 153-165 , 2012
    2012
    Citations: 28
  • Some approximation properties of Baskakov–Durrmeyer–Stancu operators
    DK Verma, V Gupta, PN Agrawal
    Applied Mathematics and Computation 218 (11), 6549-6556 , 2012
    2012
    Citations: 62
  • Rate of convergence for generalized Baskakov-Durrmeyer Operators
    DK Verma, PN Agrawal
    World Academy of Science, Engineering and Technology 71, 2050-2055 , 2012
    2012

MOST CITED SCHOLAR PUBLICATIONS

  • Some approximation properties of Baskakov–Durrmeyer–Stancu operators
    DK Verma, V Gupta, PN Agrawal
    Applied Mathematics and Computation 218 (11), 6549-6556 , 2012
    2012
    Citations: 62
  • Convergence in simultaneous approximation for Srivastava-Gupta operators
    DK Verma, PN Agrawal
    Mathematical Sciences 6 (1), 22 , 2012
    2012
    Citations: 39
  • Simultaneous approximation by certain Baskakov–Durrmeyer–Stancu operators
    V Gupta, DK Verma, PN Agrawal
    Journal of the Egyptian Mathematical Society 20 (3), 183-187 , 2012
    2012
    Citations: 33
  • Approximation by complex Baskakov-Stancu operators in compact disks
    SG Gal, V Gupta, DK Verma, PN Agrawal
    Rendiconti del Circolo Matematico di Palermo 61 (2), 153-165 , 2012
    2012
    Citations: 28
  • Approximation by complex Favard-Szász-Mirakjan-Stancu operators in compact disks
    V Gupta, D K Verma
    Mathematical Sciences 6 (1), 25 , 2012
    2012
    Citations: 24
  • Approximation for a new sequence of summation-integral type operators
    V Gupta, A Ravi P., DK Verma
    Advances in Mathematical Sciences and Applications 23 (1), 35-42 , 2013
    2013
    Citations: 21
  • Approximation for Jakimovski–Leviatan–Pǎltǎnea operators
    DK Verma, V Gupta
    ANNALI DELL'UNIVERSITA'DI FERRARA 61 (2), 367-380 , 2015
    2015
    Citations: 18
  • Approximation by a new sequence of operators involving Apostol-Genocchi polynomials
    C Prakash, DK Verma, N Deo
    Mathematica Slovaca 71 (5), 1179-1188 , 2021
    2021
    Citations: 17
  • Approximation by Baskakov-Durrmeyer-Stancu operators based on q -integers
    DK Verma, PN Agrawal
    Lobachevskii Journal of Mathematics 34 (2), 187-196 , 2013
    2013
    Citations: 11
  • On discrete q -beta operators
    V Gupta, PN Agrawal, DK Verma
    ANNALI DELL'UNIVERSITA'DI FERRARA 57 (1), 39-66 , 2011
    2011
    Citations: 6
  • Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators.
    C Prakash, DK Verma, N Deo
    Math. Found. Comput. 6 (3), 535-545 , 2023
    2023
    Citations: 5
  • Bézier variant of Bernstein–Durrmeyer blending-type operators
    C Prakash, N Deo, DK Verma
    Asian-European Journal of Mathematics 15 (06), 2250103 , 2022
    2022
    Citations: 4
  • Approximation by generalized Srivastava-Gupta operators based on certain parameter
    DK Verma
    Publications de l'Institut Mathematique 101 (115), 247-259 , 2017
    2017
    Citations: 4
  • A q-analogue of modified Beta operators
    V Gupta, PN Agrawal, DK Verma
    The Rocky Mountain Journal of Mathematics, 931-947 , 2013
    2013
    Citations: 4
  • Approximation by a new sequence of operators involving Charlier polynomials with a certain parameter
    DK Verma, V Gupta
    Modern Mathematical Methods and High Performance Computing in Science and … , 2016
    2016
    Citations: 3
  • APPROXIMATION BY APOSTOL-GENOCCHI SUMMATION-INTEGRAL TYPE OPERATORS
    C Prakash, N Deo, DK Verma
    Miskolc Mathematical Notes 24 (1), 369-382 , 2023
    2023
    Citations: 2
  • Approximation by a new sequence of operators involving Laguerre polynomials
    N Deo, K Kumar, DK Verma
    Filomat 39 (34), 12345-12360 , 2025
    2025
    Citations: 1
  • Parametric representation of integral operators for x> 0
    K Kumar, N Deo, DK Verma
    Filomat 39 (14), 4791-4805 , 2025
    2025
  • Some Approximation Properties by Sz\'asz-P{\u{a}}lt{\u{a}}nea type Operators involving the Appell Polynomials of class
    N Deo, C Prakash, DK Verma
    arXiv preprint arXiv:2308.03304 , 2023
    2023
  • Polynomials with a Certain Parameter
    DK Verma, V Gupta
    Modern Mathematical Methods and High Performance Computing in Science and … , 2016
    2016