Better error estimation for Szasz-Mirakjan-Beta operators

Abstract

In this paper, we present a modification of a sequence of mixed summation-integral type operators having Szasz and Beta basis functions in summation and integration, the so-called Szasz-Mirakjan-Beta operators. Then we show that our modified operators have a better error estimation on the interval [0, 2]. Furthermore, we give an r-th order generalization of the modified Szasz-Mirakjan-Beta operators and investigate their approximation properties.