Some Statistical Approximation based on Post-Widder operators


  • prerna Sharma Sardar Vallabh Bhai Patel University of Agriculture and Technology
  • Diwaker Sharma Modern group of institutions, Ghaziabad (U.P.), India



exact error estimation, Voronovskaya-type result, approximation estimate, over convergence phenomenon, Real and complex Post-Widder type operator


In the present paper, we study the convergence of real and modified Post-Widder operators in C, which is known as the extension of approximation of these operators from the real axis in the complex plane. In this direction, we also investigate error estimation in simultaneous approximation and a Voronovskaya-type asymptotic formula. 


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D. Agarwal, V. Gupta, Generalized hybrid operators preserving exponential functions, Asian-European J. of Math. 2019; 12(1): 1950089, 11 pages.

R.P. Agarwal, V. Gupta, On q-analogue of a complex summation integral type operators on compact disks, J. of Ineq. And Appl. 2012; 111.

G. A. Anastassiou and S. G. Gal, Geometric and approximation properties of a complex Post-Widder operator in the unit disk, Appl. Math. Letters 2006; 19: 314–319.

Z. Ditzian , V. Totik, Moduli of Smoothness, Springer, New York, 1987.

V. Gupta, A large family of linear positive operators, Rendiconti Del Circolo Matematico di Palermo 2020; Series 2, 69: 701-709.

V. Gupta, P. Maheshwari, Approximation with certain Post-Widder operators, Publications De L’institut Mathematique 2019; 105(119): 131-136.

V. Gupta, R. Yadav, Approximation by complex summation-integral type operators in compact disks, Mathematica Slovaca 2013; 63(5): 1025-1036.

P. Maheshwari (Sharma), Direct theorems for modified Baskakov operators in Lp-spaces, Demonstratio Mathematica 2009; XLII( 3): 553-565.

P. Maheshwari, Saturation theorem for the combinations of modified Beta operators in Lp spaces, Appl. Math. E-Notes 2007; 7: 32-37.

P. Maheshwari, An Inverse Result in Simultaneous Approximation Of modified Beta operators, Georgian Math. J. 2006; 13(2): 297-306.

P. Maheshwari Sharma, Iterative combinations for Srivastava-Gupta operators, Asian European J. of Math. 2021; 14(7): 2150108, 10 pages.

P. Maheshwari Sharma, M. Abid, Approximation by (p, q) Szász-Beta–Stancu operators. Arab. J. Math. 2020; 9: 191–200.

C.P. May, Saturation and inverse theorems for combinations of a class of exponential type operators, Canad. J. Math. 1976; 28: 1224-1250.

P. Sharma, Approximation by some Stancu type linear positive operators, J. of Nepal Mathematical Society, 2022; 5(2): 34-41.

D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, NJ, 1946.




How to Cite

Sharma, prerna, & Sharma, D. . (2023). Some Statistical Approximation based on Post-Widder operators. JOURNAL OF ADVANCES IN MATHEMATICS, 22, 23–29.