ON THE (DELTA,f)-LACUNARY STATISTICAL CONVERGENCE OF THE FUNCTIONS

Year 2020, Volume: 2 Issue: 1, 1 - 8, 30.04.2020

Bayram Sözbir , Selma Altundağ , Metin Basarır

Abstract

In this paper, we introduce the concept of ∆f -lacunary statistical convergence for a ∆-measurable real-valued function defined on time scale, where f is an unbounded modulus. Our motivation here is that this definition includes many well-known concepts which already exist in the literature. We also define strong ∆f -lacunary Cesaro summability on a time scale and give some results related to these new concepts. Furthermore, we obtain necessary and sufficient conditions for the equivalence of ∆f-convergence and ∆f -lacunary statistical convergence on a time scale.

Keywords

Modulus function, lacunary statistical convergence, delta measure on time scale, time scale

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