Journal of Inequalities and Applications (Feb 2019)

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

  • Yali Ding,
  • Tian-Zhou Xu

DOI
https://doi.org/10.1186/s13660-019-1973-2
Journal volume & issue
Vol. 2019, no. 1
pp. 1 – 13

Abstract

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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