General Summability Methods in the Approximation by Bernstein-Chlodovsky Operators

Abstract

In this paper, by using regular summability methods we modify the Bernstein-Chlodovsky operators in order get more general and powerful results than the classical aspects. We study Korovkin-type approximation theory on weighted spaces. As a special case, it is possible to Cesaro approximate (arithmetic mean convergence) to the test function e(2)(x) = x(2) although it fails for the classical Bernstein-Chlodovsky operators. At the end of the paper, we extend our results to the multi-dimensional case.