Approximation of Jain Operators by Statistical Convergence

Nurhayat lspir, Naokant Deo, Neha Bhardwaj

Abstract

In this paper, we consider a positive linear operators $P_{n}^{ \left[ \beta \right] }$ introduced by Jain [G.C. Jain, Approximation of functions by a new class of linear positive operators, Jour. Austral. Math. Soc. 13 (3)(1972) 271--276] with the help of Poisson type distribution and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its $A$-statistical convergence. We also compute the corresponding rate of $A$-statistical convergence for these operators.