Stability of ψ‐additive mappings: applications to nonlinear analysis

Abstract

The Hyers-Ulam stability of mappings is in development and several authors have remarked interesting applications of this theory to various mathematical problems. In this paper some applications in nonlinear analysis are presented, especially in fixed point theory. These kinds of applications seem not to have ever been remarked before by other authors.

A fixed point approach to the stability of an AQCQ-functional equation in RN-spaces

“…In addition, Kim [31] has obtained the Hyers-Ulam stability for a mixed type of quartic and quadratic functional equation. In 1996, Isac and Rassias [27] were the first to provide applications of stability theory of functional equations for the proof of new fixed point theorems with applications. By using fixed point methods, the stability problems of several functional equations have been extensively investigated by a number of authors (see [6,7,8,33,38,40,41,43]).…”

Fuzzy Stability of Quadratic-Cubic Functional Equations

“…In 1996, Isac and Rassias [10] were the first to provide applications of stability theory of functional equations for the proof of new fixed point theorems with applications.…”

APPROXIMATION OF MIXED TYPE FUNCTIONAL EQUATIONS IN pBANACH SPACES

“…During the last three decades a number of papers and research monographs have been published on various generalizations and applications of the generalized Hyers-Ulam stability to a number of functional equations and functions (see [5]- [14], [17,18,21,22] and [26]- [29]). We also refer the readers to the books [1,6,16,20,27].…”