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  and lacunary statistical convergence of order  of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Some relations between lacunary statistical convergence of order  and lacunary strong summability of order  are also given.