Αβ−STATISTICAL CONVERGENCE ON TIME SCALES

Abstract

In this paper, we introduce the concepts of $\alpha\beta-$statistical convergence and strong $\alpha \beta-$Ces\`{a}ro summability of delta measurable functions on anarbitrary time scale. Then some inclusion relations and results about these new concepts are presented. We will also investigate the relationship between statistical convergence and $\alpha \beta-$statistical convergence on a time scale.

On Rough I–αβ–Statistical Convergence of Order γ in Intuitionistic Fuzzy Normed Spaces

“…Recently, authors [30] explored the αβ-statistical convergence of order γ to investigate modified discrete operator approximation properties. For further study of αβ-statistical convergence of order γ, the readers can go through [6,8,13,28].…”

On asymptotically statistical equivalent functions on time scales

“…Since then, many researchers have moved some concepts related to statistical convergence and summability theory for sequences to the time scale calculus. [32][33][34][35][36][37][38][39][40] Quite recently, Sozbir and Altundag 41 introduced the notions of asymptotically statistical equivalence, asymptotically lacunary statistical equivalence, and strong asymptotically lacunary equivalence for non-negative two delta measurable real-valued functions defined on time scale. They also gave some results related to these concepts.…”

“…Moreover, the ideas of statistical convergence and time scale calculus was first combined by Seyyidoglu and Tan 30 and Turan and Duman, 31 independently. Since then, many researchers have moved some concepts related to statistical convergence and summability theory for sequences to the time scale calculus 32–40 . Quite recently, Sozbir and Altundag 41 introduced the notions of asymptotically statistical equivalence, asymptotically lacunary statistical equivalence, and strong asymptotically lacunary equivalence for non‐negative two delta measurable real‐valued functions defined on time scale.…”