Additive rho-functional inequalities in bets-homogeneous normed spaces

Abstract

Abstract. In this paper, we solve the following additive -functional inequalities k f (x + y) 􀀀 f (x) 􀀀 f (y)k

2 f x + y 2

􀀀 f (x) + 􀀀f (y)

; (1) where is a fixed complex number with j j < 1, and

2 f x + y 2

􀀀 f (x) 􀀀 f (y)

k ( f (x + y) 􀀀 f (x) 􀀀 f (y))k; (2) where is a fixed complex number with j j < 1 2 , and prove the Hyers-Ulam stability of the additive - functional inequalities (1) and (2) in -homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive -functional equations associated with the additive -functional inequalities (1) and (2) in -homogeneous complex Banach spaces.