{\Delta}- convergence on time scale

TL;DR

This paper introduces new notions of { ext{ extDelta}}-convergence and { ext{ extDelta}}-Cauchy using { ext{ extDelta}}-density, generalizing existing results in statistical convergence theory.

Contribution

It proposes novel concepts of { ext{ extDelta}}-convergence and { ext{ extDelta}}-Cauchy, expanding the theoretical framework of convergence using { ext{ extDelta}}-density.

Findings

{ ext{ extDelta}}-convergence generalizes statistical convergence.

The paper establishes relationships between { ext{ extDelta}}-convergence and { ext{ extDelta}}-Cauchy.

Results extend existing convergence theories.

Abstract

In the present paper we will give some new notions, such as {\Delta}-convergence and {\Delta}-Cauchy, by using the {\Delta}-density and investigate their relations. It is important to say that, the results presented in this work generalize some of the results mentioned in the theory of statistical convergence.