On the Generalized Stabilities of Functional Equations via Isometries

Abstract

The main goal of this research article is to investigate the stability of generalized norm-additive functional equations. This study demonstrates that these equations are Hyers-Ulam stable for surjective functions from an arbitrary group G to a real Banach space B using the large perturbation method. Furthermore, hyperstability results are investigated for a generalized Cauchy equation.

Keywords

• functional equations
• Banach space
• isometries
• stability analysis
• norm-additive FE
• large perturbation method