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On Set-Valued Solutions of a Generalized Bi-quadratic Functional Equation

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Abstract

In this article, we obtain a characterizations and representations of set-valued solutions defined on an Abelian group G with values in a Hausdorff topological vector space of the following generalized bi-quadratic functional equation:

$$\begin{aligned}&F(x+y,z+w)+F(x+y,z-w)+F(x-y,z+w)+F(x-y,z-w) \\&\quad =aF(x,z)+bF(x,w)+cF(y,z)+dF(y,w), \end{aligned}$$

for some nonnegative real numbers abc,  and d.

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Correspondence to Iz-iddine EL-Fassi.

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EL-Fassi, Ii., El-Hady, ES. & Nikodem, K. On Set-Valued Solutions of a Generalized Bi-quadratic Functional Equation. Results Math 75, 89 (2020). https://doi.org/10.1007/s00025-020-01225-0

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