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Title: Practical Ulam-Hyers-Rassias stability for nonlinear equations (English)
Author: Wang, Jin Rong
Author: Fečkan, Michal
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 142
Issue: 1
Year: 2017
Pages: 47-56
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: practical Ulam-Hyers-Rassias stability
Keyword: nonlinear equation
MSC: 39B82
MSC: 46T20
MSC: 47H10
MSC: 47H99
MSC: 47J05
idZBL: Zbl 06738569
idMR: MR3619986
DOI: 10.21136/MB.2017.0058-14
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Date available: 2017-02-21T17:21:22Z
Last updated: 2018-04-02
Stable URL: http://hdl.handle.net/10338.dmlcz/146008
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