A note on rough statistical convergence

TL;DR

This paper introduces new concepts of rough statistical convergence and rough statistically Cauchy sequences for real-valued functions, exploring their properties and equivalence.

Contribution

It defines and analyzes the notions of pointwise rough statistical convergence and rough statistically Cauchy sequences, extending existing convergence theories.

Findings

Established the equivalence between the introduced concepts.

Provided foundational properties of rough statistical convergence.

Extended classical convergence notions to a rough statistical context.

Abstract

In this paper, we introduce the notions of pointwise rough statistical convergence and rough statistically Cauchy sequences of real valued functions in the line of A. (T$\ddot{u}$rkmenoglu) G$\ddot{o}$khan and M. G$\ddot{u}$ng$\ddot{o}$r \cite{Tu1}. Furthermore we study thier equivalence.