Approximation by Bivariate Szasz-Mirakyan Operators Preserving E-2(p1+p2)

Abstract

The present paper is dedicated to the modification of the bivariate generalized Szasz-Mirakyan operators while preserving the exponential functions exp(2, 2) where exp(tau(1), tau(2)) = e(-tau 1p1 - tau 2p2), tau(1), tau(2) is an element of R-0(+) , and p(1), p(2) >= 0. We thoroughly investigate the weighted approximation properties and also obtain the convergence rate for these operators by utilizing a weighted modulus of continuity. Additionally, we delve into the order of approximation by investigating local approximation results through Peetre's K-functional. Furthermore, we present the GBS (Generalized Boolean Sum) operators of Szasz-Mirakyan operators and obtain the order of approximation in terms of the Lipschitz class of Bogel continuous functions and the mixed modulus of smoothness. In order to enhance our theoretical findings and effectively showcase the efficiency of our developed operators, we have included a wide range of numerical examples using various values.