Displaying similar documents to “A fixed point approach to the stability of differential equations y ' = F ( x , y ) .”

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...