Stability of involutions on Banach Algebra by fixed point method

TL;DR

This paper investigates the stability of involutions on Banach algebras using fixed point methods, establishing conditions under which approximate involutions lead to $C^*$-algebras.

Contribution

It introduces a fixed point approach to analyze the stability of involutions and identifies conditions for approximate involutions to imply $C^*$-algebra structure.

Findings

Proved Hyers-Ulam-Rassias stability of involutions

Established super stability of involutions

Identified conditions for approximate involutions to form $C^*$-algebras

Abstract

Using the fixed point method of the stability of the Jensen's functional equation, we proved the Hyers-Ulam-Rassias stability and super stability of involution on Banach algebra and find some conditions that with them a Banach algebra with approximate involution is $C^*$-algebra.