On the Generalized Stabilities of Functional Equations via Isometries
Muhammad Sarfraz,
Jiang Zhou,
Yongjin Li,
John Michael Rassias
Affiliations
Muhammad Sarfraz
School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Jiang Zhou
School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Yongjin Li
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
John Michael Rassias
The Pedagogical Department of Primary Education Section of Mathematics and Informatics, The National and Capodistrian University of Athens, 15342 Athens, Greece
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.
