Practical Ulam-Hyers-Rassias stability for nonlinear equations

Jin Rong Wang; Michal Fečkan

Mathematica Bohemica (2017)

  • Volume: 142, Issue: 1, page 47-56
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Wang, Jin Rong, and Fečkan, Michal. "Practical Ulam-Hyers-Rassias stability for nonlinear equations." Mathematica Bohemica 142.1 (2017): 47-56. <http://eudml.org/doc/287897>.

@article{Wang2017,
abstract = {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.},
author = {Wang, Jin Rong, Fečkan, Michal},
journal = {Mathematica Bohemica},
keywords = {practical Ulam-Hyers-Rassias stability; nonlinear equation},
language = {eng},
number = {1},
pages = {47-56},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Practical Ulam-Hyers-Rassias stability for nonlinear equations},
url = {http://eudml.org/doc/287897},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Wang, Jin Rong
AU - Fečkan, Michal
TI - Practical Ulam-Hyers-Rassias stability for nonlinear equations
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 1
SP - 47
EP - 56
AB - 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.
LA - eng
KW - practical Ulam-Hyers-Rassias stability; nonlinear equation
UR - http://eudml.org/doc/287897
ER -

References

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