Lacunary statistical convergence of Bernstein operator sequences

Abstract

The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. Recently the statistical convergence of Bernstein operators was studied. In this paper, by using the concept of natural density and lacunary sequences we first introduce the notion of lacunary statistical convergence of a sequence of Bernstein polynomials. Next we apply this notion to V-B(theta)-summability. We also investigate some inclusion relations related to these concepts. (C) 2017 The Authors. Published by IASE. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).