A fixed point application for the stability and hyperstability of multi-Jensen-quadratic mappings
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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.
KeywordsBanach space Multi-Jensen mapping Multi-quadratic mapping Hyers–Ulam stability
Mathematics Subject Classification39B52 39B72 39B82 46B03
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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