Summability Process by Mastroianni Operators and Their Generalizations

Abstract

In this paper, we prove a general Korovkin-type approximation theorem for the Mastroianni operators using a regular summability process with non-negative entries. We also obtain some useful estimates via the modulus of continuity and the second modulus of smoothness. Furthermore, we construct a sequence of Szasz-Mirakjan type operators satisfying a Voronovskaja-type property such that it is possible to approximate a function by these operators in the sense of summation process, although their classical approximation fails.