On Bernstein-Chlodovsky operators preserving $e^{-2x} $

Abstract

In this paper we introduce a generalization of Bernstein-Chlodovsky operators that preserves the exponential function $e^{-2x}$ $(x \geq 0)$. We study its approximation properties in several function spaces, and we evaluate the rate of convergence by means of suitable moduli of continuity. Throughout some estimates of the rate of convergence, we prove better error estimation than the original operators on certain intervals.