Weakly Symmetrically Continuous Functions

TL;DR

This paper extends the concept of weak symmetric continuity to functions on any subset of real numbers, explores their properties, compares them with related continuity types, and provides illustrative examples.

Contribution

It introduces a generalized definition of weak symmetric continuity for functions on arbitrary subsets of , and analyzes their fundamental properties and relationships.

Findings

Weakly symmetrically continuous functions have distinct properties from symmetric and weakly continuous functions.

Several examples demonstrate the differences and applications of these functions.

Basic properties and comparisons are established for the extended definition.

Abstract

We extend the definition of weak symmetric continuity to be applicable for functions defined on any nonempty subset of $\R$. Then we investigate basic properties of weakly symmetrically continuous functions and compare them with those of symmetrically continuous functions and weakly continuous functions. Several examples are also given.