Quadratic ρ-functional inequalities in banach spac

Abstract

In this paper, we solve the following quadratic ρ-functional inequalities (Formula Presented) where ρ is a fixed complex number with |ρ| < (Formula Presented) and (Formula Presented) where ρ is a fixed complex number with |ρ|<4 Using the direct method, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces.