A generalization of the Hyers–Ulam–Rassias stability of the Pexiderized quadratic equations

Abstract

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approx-

Fuzzy Stability of an Aqcq-Functional Equation in Matrix Fuzzy Normed Spaces

“…The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [1,3,24,31,34,35,39,42,44,50,66,57], [60]- [62]). …”

Ulam's Stabilities of Fractional Integro-Differential Equations

“…In 1978, Rassias [3] provided a remarkable generalization of the Ulam-Hyers stability of mappings by considering variables. During the last two decades very important contirbutions to the stability problems of functional equations were given by many mathematicians (see [4][5][6][7][8][9][10][11]). A generalization of Ulam's problem was recently proposed by replacing functional equations with differential equations: The differential equation F (t, y(t), y ′ (t), ..., y (n) (t)) = 0 has the Hyers-Ulam stability if for given ε > 0 and a function y such that…”

Functional Inequalities in Paranormed Spaces

“…Rassias' Theorem. During the last two decades a number of papers and research monographs have been published on various generalizations and applications of the Hyers-Ulam stability to a number of functional equations and mappings (see [12,13,18]). …”