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A fixed point application for the stability and hyperstability of multi-Jensen-quadratic mappings

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Abstract

In this paper, we unify the system of functional equations defining a multi-Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers–Ulam stability of such equation and thus generalizing some known results. As a result, we show that the multi-Jensen-quadratic functional equation is hyperstable.

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Acknowledgements

The authors sincerely thank the anonymous reviewer for his/her careful reading, constructive comments and suggesting some related references to improve the quality of the first draft. They also would like to thank Dr. Sang Og Kim for pointing out the result in Lemma 3.1 is not correct for \(k=n\).

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Correspondence to Abasalt Bodaghi.

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Cite this article

Salimi, S., Bodaghi, A. A fixed point application for the stability and hyperstability of multi-Jensen-quadratic mappings. J. Fixed Point Theory Appl. 22, 9 (2020). https://doi.org/10.1007/s11784-019-0738-3

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Keywords

  • Banach space
  • Multi-Jensen mapping
  • Multi-quadratic mapping
  • Hyers–Ulam stability

Mathematics Subject Classification

  • 39B52
  • 39B72
  • 39B82
  • 46B03