On rough continuity and rough $I$-continuity of real functions

TL;DR

This paper explores various notions of rough continuity and rough I-continuity for real functions, establishing their properties and relationships, and introduces new concepts like rough (I1, I2)-continuity and rough I*-continuity.

Contribution

It introduces and analyzes new types of rough continuity, expanding the theoretical framework for understanding real functions' continuity under rough and I-continuity concepts.

Findings

Established properties of rough continuity

Analyzed relations between rough I-continuity and rough continuity

Introduced rough (I1, I2)-continuity and rough I*-continuity

Abstract

In this paper, we have studied first the idea of rough continuity of real valued functions of real variables and then we have discussed some important properties of rough continuity. Then we study the idea of rough $I$-continuity of real valued functions and find the relation between rough $I$-continuity and rough continuity. We also introduce the notion of rough $(I_1, I_2)$-continuity and rough $I^*$-continuity of real valued functions and discuss some properties on this two types on continuity.