The Hyers theorem via the Markov–Kakutani fixed point theorem

Przebieracz, Barbara

doi:10.1007/s11784-013-0102-y

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Theorem 25 Let Be a Linear Topological Space And Let ⊂ Be A1

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“…Theorem 25 has been applied in [41] to provide an alternative (quite involved) proof of the following classical stability result due to Hyers [2].…”

Section: Theorem 25 Let Be a Linear Topological Space And Let ⊂ Be Amentioning

confidence: 99%

Fixed Point Theory and the Ulam Stability

Brzdęk

Cădariu

Ciepliński

2014

Journal of Function Spaces

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The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving 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 stability of functional equations, motivated by a problem raised by Ulam in 1940.

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“…Theorem 25 has been applied in [41] to provide an alternative (quite involved) proof of the following classical stability result due to Hyers [2].…”

Section: Theorem 25 Let Be a Linear Topological Space And Let ⊂ Be Amentioning

confidence: 99%