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 → Y satisfies f ( x + i y ) + f ( x - i y ) = 2 f ( x ) - 2 f ( y ) for all x , y ∈ X , then the mapping f : X → Y satisfies f ( x + y ) + f ( x - y ) = 2 f ( x ) + 2 f ( y ) for all x , y ∈ 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.