Approximation of involution in multi-Banach algebras: Fixed point technique

Abstract

In this research work, we demonstrate the Hyers-Ulam stability for Cauchy-Jensen functional equation in multi-Banach algebras by the fixed point technique. In fact, we prove that for a function which is approximately Cauchy-Jensen in multi Banach algebra, there is a unique involution near it. Next, we show that under some conditions the involution is continuous, the multi-Banach algebra becomes multi-C∗-algebra and the Banach algebra is self-adjoint.

Keywords

• multi-banach algebra
• hyers-ulam stability
• functional equation
• fixed point technique
• c∗-algebra