Blending type Approximation of Generalized Lupa\c{s}-Jain type Operators via $A$-Statistical Convergence and Power Series Method

Abstract

In this paper, we introduce integral type modification of generalized Lupa\c{s} operators as presented by Goyal and Kajla \cite{GO}. In a weighted space, we explore how these operators approximate by employing both the $A$-statistical method and the power series method. We establish a generalization of the Lupa\c{s}-Jain type operators of order $\kappa$ with the help of methodology that Kirov and Popova \cite{KI} used, and estimate the approximation error for a function of Lipschitz class. Using Maple software, we obtain error of approximation of newly defined operators to certain functions.