Hyers-Ulam stability for a nonlinear iterative equation

Bing Xu; Weinian Zhang

Displaying similar documents to “Hyers-Ulam stability for a nonlinear iterative equation”

Practical Ulam-Hyers-Rassias stability for nonlinear equations

Jin Rong Wang, Michal Fečkan (2017)

Mathematica Bohemica

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In this paper, we offer a new stability concept, practical Ulam-Hyers-Rassias stability, for nonlinear equations in Banach spaces, which consists in a restriction of Ulam-Hyers-Rassias stability to bounded subsets. We derive some interesting sufficient conditions on practical Ulam-Hyers-Rassias stability from a nonlinear functional analysis point of view. Our method is based on solving nonlinear equations via homotopy method together with Bihari inequality result. Then we consider nonlinear...

Nonlinear stability of a quadratic functional equation with complex involution

Reza Saadati, Ghadir Sadeghi (2011)

Archivum Mathematicum

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Let $X, Y$ be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping $f : X \to Y$ satisfies $\begin{matrix} f (x + i y) + f (x - i y) = 2 f (x) - 2 f (y) \end{matrix}$ for all $x$ , $y \in X$ , then the mapping $f : X \to Y$ satisfies $f (x + y) + f (x - y) = 2 f (x) + 2 f (y)$ for all $x$ , $y \in X$ . Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method.