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http://dx.doi.org/10.4134/CKMS.c200238

HYPERSTABILITY CRITERION FOR A NEW TYPE OF 2-VARIABLE RADICAL FUNCTIONAL EQUATIONS  

EL-Fassi, Iz-iddine (Department of Mathematics Faculty of Sciences and Techniques Sidi Mohamed ben abdellah University)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.2, 2021 , pp. 343-359 More about this Journal
Abstract
The aim of this paper is to obtain the general solution of the 2-variable radical functional equations $f({\sqrt[k]{x^k+z^k}},\;{\sqrt[{\ell}]{y^{\ell}+w^{\ell}}})=f(x,y)+f(z,w)$, x, y, z, w ∈ ℝ, for f a mapping from the set of all real numbers ℝ into a vector space, where k and ℓ are fixed positive integers. Also using the fixed point result of Brzdęk and Ciepliński [11, Theorem 1] in (2, 𝛽)-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, ${\beta}$)-normed space; two-variable radical functional equation; fixed point theorem;
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