General Family of Exponential Operators

Abstract

In this article, we deal with the approximation properties of Ismail-May operators \cite{IM:78} based on a non-negative real parameter $\lambda$. We provide some graphs and error estimation table for a numerical example depicting the convergence of our proposed operators. We further define the B\'{e}zier variant of these operators and give a direct approximation theorem using Ditizan-Totik modulus of smoothness and a Voronovoskaya type asymptotic theorem. We also study the error in approximation of functions having derivatives of bounded variation. Lastly, we introduce the bivariate generalization of Ismail May operators and estimate its rate of convergence for functions of Lipschitz class.