Chlodowsky variant of generalised Jain-Appell operators

Abstract

In this paper, we consider Chlodowsky variant of Jain-Appell operators which includes many known and new defined operators such as Chlodowsky variant of generalised Jakimovski-Leviatan, Jain-Appell, Appell-Baskakov and Appell-Lupaş operators. These operators are constructed in terms of the function ϱ and their weighted approximation to the identity operator is given in the weighted space with weight φ = 1 + ϱ^2 by using the Korovkin set {1, ϱ, ϱ^2}. We investigate a quantitative error estimate of the operators by using Holhos’ weighted modulus of continuity and obtain the local approximation properties in terms of the first and the second modulus of continuities and Lipschitz class maximal function. Furthermore, the Voronovskaja type asymptotic formula is also obtained.