Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2-Banach spaces

Abstract

Abstract In this paper, using Brzdȩk and Ciepliński’s fixed point theorems in a 2-Banach space, we investigate approximate solution for the generalized inhomogeneous radical quadratic functional equation of the form f(ax2+by2)=af(x)+bf(y)+D(x,y), $$f \bigl(\sqrt{ax^{2}+by^{2}} \bigr)=af(x)+bf(y) + D(x,y), $$ where f is a mapping on the set of real numbers, a,b∈R+ $a, b\in\mathbf {R}_{+}$ and D(x,y) $D(x,y)$ is a given function. Some stability and hyperstability properties are presented.

Keywords

• Fixed point theorem
• Hyperstability
• Radical quadratic functional equation
• 2-Banach space