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Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach

  • Abasalt Bodaghi EMAIL logo
Published/Copyright: January 29, 2021
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Abstract

In this article, by using a new form of multi-quadratic mapping, we define multi-m-Jensen-quadratic mappings and then unify the system of functional equations defining a multi-m-Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of multi-quadratic and multi-m-Jensen-quadratic functional equations. As a consequence, we show that every multi-m-Jensen-quadratic functional equation (under some conditions) can be hyperstable.

MSC 2010: 39B52; 39B72; 39B82; 46B03

Acknowledgement

The author sincerely thank the anonymous reviewer for his/her careful reading, constructive comments and suggestions to improve the quality of the first draft of paper.

  1. (Communicated by Gregor Dolinar)

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Received: 2019-08-20
Accepted: 2020-06-26
Published Online: 2021-01-29
Published in Print: 2021-02-23

© 2021 Mathematical Institute Slovak Academy of Sciences

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