The Cauchy–Optimal Stability Results for Cauchy–Jensen Additive Mappings in the Fuzzy Banach Space and the Unital Fuzzy Banach Space

Abstract

In this article, we apply a new class of fuzzy control functions to approximate a Cauchy additive mapping in fuzzy Banach space (FBS). Further, considering the unital FBS (UFBS), we will investigate the isomorphisms defined in this space. By introducing several specific functions and choosing the optimal control function from among these functions, we evaluate the Cauchy–Optimal stability (C–O-stability) for all defined mappings.

Keywords

• Cauchy additive mapping
• Jensen additive mapping
• stability
• isomorphism
• fuzzy Banach space
• unital space