Generalized Hyers‐Ulam‐Rassias Theorem in Menger Probabilistic Normed Spaces

Abstract

We introduce two reasonable versions of approximately additive functions in a Šerstnev probabilistic normed space endowed with triangle function. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in above mentioned spaces.

General Solution and Stability of Additive-Quadratic Functional Equation in IRN-Space

“…As of late, Zhang [23] examined the cubic functional equation in intuitionistic random space. The stability of various equations in RN-spaces has been as of late concentrated in Alsina [24], Eshaghi Gordji et al [25,26], , and Saadati et al [30]. Xu et al [31][32][33] presented the various mixed types of functional equations investigated in Intuitionistic fuzzy normed spaces, quasi Banach spaces, and random normed spaces.…”

A General System of Nonlinear Functional Equations in Non-Archimedean Spaces

“…In 1994, a generalization of the Rassias theorem was obtained by Gävruta[ll] by replacing the unbounded Cauchy difference by a general control function. In recent years many authors have investigated the stability of various functional equations in various spaces (see for instance [4,6,7,8,12,16,17,21,26,27]). …”

Random Stability of Quadratic Functional Equations a Fixed Point Approach

“…Czerwik [7] proved the generalized Hyers-Ulam stability of the quadratic functional equation. 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 [1,8,11,15,17], [32]- [38]).…”