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

Authors : Bayram SÖZBİR, Selma ALTUNDAĞ, Metin BASARIR

Pages : 1-8

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Publication Date : 2020-04-30

Article Type : Research Paper

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