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In this paper, we solve the following quadratic ρ-functional inequalities ‖f(x+ y)+f(x− y)− 2f(x)− 2f(y)‖ ≤ ‖ρ(2f( y 2 ) + 2f( x− y 2 )− f(x)− f(y))‖, where ρ is a fixed complex number with |ρ| < 1, and ‖2f( y 2 )+2f( x− y 2 )− f(x)− f(y)‖ ≤ ‖ρ(f(x+ y) + f(x− y)− 2f(x)− 2f(y))‖, where ρ is a fixed complex number with |ρ| < 12 . By using the direct method, we prove the Hyers-Ulam stability of these inequalities in complex matrix normed spaces, and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with these inequalities in complex matrix normed spaces. c ©2016 All rights reserved.

Quadratic ρ -functional inequalities in complex matrix normed spaces