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Generalized hyperstability of a Drygas functional equation on a restricted domain using Brzdęk’s fixed point theorem

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Abstract

Motivated by the notion of Ulam stability, we investigate the generalized hyperstability results for the Drygas functional equation

$$\begin{aligned} f(x+y)+f(x-y)=2f(x)+f(y)+f(-y), \end{aligned}$$

on a restricted domain. The method is based on a quite recent fixed point theorem (cf. [6, Theorem 1]) in some functions spaces. We derive from them some characterizations of inner product spaces. Our results are improvements and generalizations of the main results of Piszczek and Szczawińska [29].

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Acknowledgements

The author would like to thank the anonymous referee for his careful reading and valuable suggestions to improve the quality of the paper. Also, my sincere regards and gratitude go to Professor Janusz Brzdęk for many information and discussions on the hyperstability of functional equations.

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  1. Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, Kenitra, Morocco

    Iz-iddine EL-Fassi

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  1. Iz-iddine EL-Fassi
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Correspondence to Iz-iddine EL-Fassi.

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EL-Fassi, Ii. Generalized hyperstability of a Drygas functional equation on a restricted domain using Brzdęk’s fixed point theorem. J. Fixed Point Theory Appl. 19, 2529–2540 (2017). https://doi.org/10.1007/s11784-017-0439-8

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