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http://dx.doi.org/10.7468/jksmeb.2016.23.2.155

ADDITIVE ρ-FUNCTIONAL INEQUALITIES  

LEE, SUNG JIN (DEPARTMENT OF MATHEMATICS, DAEJIN UNIVERSITY)
LEE, JUNG RYE (DEPARTMENT OF MATHEMATICS, DAEJIN UNIVERSITY)
SEO, JEONG PIL (OHSANG HIGH SCHOOL)
Publication Information
The Pure and Applied Mathematics / v.23, no.2, 2016 , pp. 155-162 More about this Journal
Abstract
In this paper, we solve the additive ρ-functional inequalities (0.1)${\parallel}f(x+y)+f(x-y)-2f(x){\parallel}$ $\leq$ ${\parallel}{\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$, where ρ is a fixed complex number with |ρ| < 1, and (0.2) ${\parallel}2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$ $\leq$ ${\parallel}{\rho}f(x+y)+f(x-y)-2f(x){\parallel}$, 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
Hyers-Ulam stability; additive ρ -functional inequality;
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