Lacunary statistical convergence and strongly lacunary summable functions of order α

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