HYPERSTABILITY CRITERION FOR A NEW TYPE OF 2-VARIABLE RADICAL FUNCTIONAL EQUATIONS
Commun. Korean Math. Soc.
Published online September 14, 2020
Iz-iddine EL-Fassi
Department of Mathematics, Faculty of Sciences and Techniques, Sidi Mohamed Ben Abdellah University, B.P. 2202, Fez, Morocco
Abstract : The aim of this paper is to obtain the general solution of the 2-variable radical functional equations
$$f\left(\sqrt[k]{x^{k}+z^{k}} ,\sqrt[\ell]{y^{\ell}+w^{\ell}}\right)=f(x,y)+f(z,w),\;\;\;x,y,z,w\in \mathbb{R},
$$for $f$ a mapping from the set of all real numbers $\mathbb{R}$ into a vector space, where $k$ and $\ell$ are fixed positive integers. Also using the fixed point result of Brzd\k{e}k and Ciepli\'{n}ski \cite[Theorem 1]{krs} in $(2,\beta)$-Banach spaces, we prove the generalized hyperstability results of the 2-variable radical functional equations. In the end of this paper we derive some consequences from our main results.
Keywords : Hyperstability; (2, β)-normed space; Two-variable radical functional equation; Fixed point theorem.
MSC numbers : Primary 39B82, 39B62; Secondary 65Q20, 47H10.
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