Approximation and analysis regarding the structure of a multiple variable mapping

Abasalt Bodaghi; Maryam Mosleh; Hemen Dutta

doi:10.5269/bspm.63002

Abasalt Bodaghi Islamic Azad University https://orcid.org/0000-0003-0358-4518
Maryam Mosleh Islamic Azad University https://orcid.org/0000-0003-3553-6596
Hemen Dutta Gauhati University https://orcid.org/0000-0003-2765-2386

Abstract

The article introduces a several variables mapping as the multimixed quadratic-cubic mapping in order to characterize such mappings. It reduces a system of equations defining the multimixed quadratic-cubic mappings to obtain a single functional equation. It is shown that under some mild conditions, every multimixed quadratic-cubic mapping can be multi-quadratic, multi-cubic and multiquadratic-cubic. Further, the generalized Hyers-Ulam stability and hyperstabilty for multimixed quadratic-cubic functional equations in quasi-$\beta$ normed spaces have been investigated.

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