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

  • Somaye Salimi
  • Abasalt BodaghiEmail author
Article
  • 21 Downloads

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.

Keywords

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

Mathematics Subject Classification

39B52 39B72 39B82 46B03 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Qazvin BranchIslamic Azad UniversityQazvinIran
  2. 2.Department of Mathematics, Garmsar BranchIslamic Azad UniversityGarmsarIran

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