Generalized Hyers-Ulam Type Stability of the $2k$-Variables Quadratic $\beta$-Functional Inequalities And Function in $\gamma$-Homogeneous Normed Space

Abstract

In this paper, we study to solve two quadratic $\beta$-functional inequalities with $2k$-variables in $\gamma$-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of quadratic $\beta$-functional equations associated two the quadratic $\beta$-functional inequalities in $\gamma$-homogeneous complex Banach spaces. We will show that the solutions of the first and second inequalities are quadratic mappings.