A fixed point approach to the hyers-ulam stability of a functional equation in various normed spaces

Abstract

Using direct method, Kenary (Acta Universitatis Apulensis, to appear) proved the Hyers-Ulam stability of the following functional equationin non-Archimedean normed spaces and in random normed spaces, where m, n are different integers greater than 1. In this article, using fixed point method, we prove the Hyers-Ulam stability of the above functional equation in various normed spaces.

Two methods of generalized Ulam-Hyers stability of a quattuorvigintic functional equation in various Banach spaces

“…During the last seven decades, the stability problems of a variety of functional equations in quite a lot of spaces have been broadly investigated by number of mathematicians [3,5,8,12,15,17,22,27,32,34,36,39,42].…”

On the Complete 2-Normed Stabilization of Cubic and Quadratic Functional Equations

“…The stability of Equation (2) was studied by Kenary et.al. 7 via fixed point approach. It was Park 14 who investigated the stabilization of functional equations in complete 2-normed spaces.…”

On the Hyers-Ulam stabilities of functional equations on n-Banach spaces

“…the general solution and generalized Hyers-Ulam stability were established by Chang and Kim [2]. By a direct method of fixed points, Kenary et al [15] obtained the generalized Hyers-Ulam stability for a quadratic functional equation…”