Practical Ulam-Hyers-Rassias stability for nonlinear equations
Mathematica Bohemica, Tome 142 (2017) no. 1, pp. 47-56.

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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 equations with surjective asymptotics at infinity. Moore-Penrose inverses are used for equations defined on Hilbert spaces. Specific practical Ulam-Hyers-Rassias results are derived for finite-dimensional equations. Finally, two examples illustrate our theoretical results.
DOI : 10.21136/MB.2017.0058-14
Classification : 39B82, 46T20, 47H10, 47H99, 47J05
Mots-clés : practical Ulam-Hyers-Rassias stability; nonlinear equation 
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Wang, Jin Rong; Fečkan, Michal. Practical Ulam-Hyers-Rassias stability for nonlinear equations. Mathematica Bohemica, Tome 142 (2017) no. 1, pp. 47-56. doi : 10.21136/MB.2017.0058-14. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2017.0058-14/

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