• Journal title : The Pure and Applied Mathematics
• Volume 23, Issue 2,  2016, pp.155-162
• Publisher : Korea Society of Mathematical Education
• DOI : 10.7468/jksmeb.2016.23.2.155
Title & Authors
LEE, SUNG JIN; LEE, JUNG RYE; SEO, JEONG PIL;

Abstract
In this paper, we solve the additive ρ-functional inequalities (0.1)$\small{{\parallel}f(x+y)+f(x-y)-2f(x){\parallel}}$ $\small{\leq}$ $\small{{\parallel}{\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}}$, where ρ is a fixed complex number with |ρ| < 1, and (0.2) $\small{{\parallel}2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}}$ $\small{\leq}$ $\small{{\parallel}{\rho}f(x+y)+f(x-y)-2f(x){\parallel}}$, where ρ is a fixed complex number with |ρ| < 1. Furthermore, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces.
Keywords
Language
English
Cited by
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