A fixed point approach to the stability of the functional equation .
Jung, Soon-Mo, Min, Seungwook (2009)
Fixed Point Theory and Applications [electronic only]
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Jung, Soon-Mo, Min, Seungwook (2009)
Fixed Point Theory and Applications [electronic only]
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International Journal of Mathematics and Mathematical Sciences
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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...