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Multi-quadratic mappings with an involution

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Abstract

In this article, by using a quadratic functional equation with an involution, defined by Stetkær, we introduce a new class of multi-quadratic mappings and then describe them as an equation. Moreover, we establish the Hyers–Ulam stability of multi-quadratic mappings in normed spaces by applying the Diaz-Margolis fixed point alternative. In addition, we present a direct consequence of the Hyers−Ulam stability of multi-quadratic mappings in the setting of normed \(*\)-algebras.

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Acknowledgements

The author sincerely thanks the anonymous reviewer for his/her careful reading, constructive comments, and suggesting some related references to improve the quality of the first draft of paper.

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  1. Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran

    Abasalt Bodaghi

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  1. Abasalt Bodaghi
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Correspondence to Abasalt Bodaghi.

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Communicated by Abasalt Bodaghi.

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Bodaghi, A. Multi-quadratic mappings with an involution. J Anal 30, 859–870 (2022). https://doi.org/10.1007/s41478-021-00375-w

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