Stability of a General Functional Equation in m-Banach Spaces

Abstract

In this note, the Ulam stability of a general functional equation in several variables is investigated. It is shown that this equation is Ulam stable in m-Banach spaces. Since a particular case of the considered equation is, among others, a functional equation introduced by Ji et al. and Zhao et al. for a characterization of the so-called multi-quadratic mapping, a result on its stability is also presented. Moreover, some other applications are provided.

New random version of stability via fixed point method

“…The topic of stability, which was inquiry from S.M.Ulam [10] in1940 expanded hugely in numerous spaces and using different equations. Mathematicians scientists have accomplished success in various ways, including fixed point method [1,2,6,7,8,9,11,12]. The stability of many other functional equations where also investigated in random normed spaces[ȐṄ −space ].…”