Approximate Solution of P-Radical Functional Equation in 2-Banach Spaces

Muaadh Almahalebi; Abdellatif Chahbi

doi:10.1007/s10473-019-0218-2

Approximate Solution of P-Radical Functional Equation in 2-Banach Spaces

Muaadh Almahalebi, Abdellatif Chahbi

Source

Acta Mathematica Scientia > 2019 > 39 > 2 > 551-566

Abstract

The aim of this paper is to introduce and solve the p-radical functional equation $$f\left( {\sqrt[p]{{x^p + y^p }}} \right) = f\left( x \right) + f\left( y \right),p \in \mathbb{N}_2 .$$ f ( x p + y p p ) = f ( x ) + f ( y ) , p ∈ N 2 . We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.