Applications of fixed point theorems to the Hyers-Ulam stability of functional equations–a survey
The fixed point method, which is the second most popular technique of proving the Hyers-Ulam stability of functional equations, was used for the first time in 1991 by J.A. Baker who applied a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single va...
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| Published in | Annals of functional analysis Vol. 3; no. 1; pp. 151 - 164 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Springer
01.01.2012
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| Online Access | Get full text |
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| Summary: | The fixed point method, which is the second most popular technique of proving the Hyers-Ulam stability of functional equations, was used for the first time in 1991 by J.A. Baker who applied a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow Radu's approach and make use of a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of the Hyers-Ulam stability of functional equations. 2010 Mathematics Subject Classification. Primary 39B82; Secondary 47H10, 46S10. Key words and phrases. Hyers-Ulam stability, functional equation, fixed point theorem, ultrametric. |
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| ISSN: | 2008-8752 2008-8752 |
| DOI: | 10.15352/afa/1399900032 |