Lacunary Statistical Convergence and Strongly Lacunary Summable Functions of Order ?

Abstract

The main purpose of this paper is to introduce and investigate the concepts of lacunary strong summability of order alpha and lacunary statistical convergence of order alpha of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,infinity). Some relations between lacunary statistical convergence of order alpha and lacunary strong summability of order beta are also given.