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

The aim of this paper is to introduce and solve the p-radical functional equation $$f\left( {\sqrt[p]{{x^p + y^p }}} \right) = f\left( x \right) + f\left( y \right),p \in \mathbb{N}_2 .$$ 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.