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http://dx.doi.org/10.7468/jksmeb.2016.23.3.319

ADDITIVE ρ-FUNCTIONAL INEQUALITIES IN β-HOMOGENEOUS F-SPACES  

LEE, HARIN (MATHEMATICS BRANCH, SEOUL SCIENCE HIGH SCHOOL)
CHA, JAE YOUNG (MATHEMATICS BRANCH, SEOUL SCIENCE HIGH SCHOOL)
CHO, MIN WOO (MATHEMATICS BRANCH, SEOUL SCIENCE HIGH SCHOOL)
KWON, MYUNGJUN (MATHEMATICS BRANCH, SEOUL SCIENCE HIGH SCHOOL)
Publication Information
The Pure and Applied Mathematics / v.23, no.3, 2016 , pp. 319-328 More about this Journal
Abstract
In this paper, we solve the additive ρ-functional inequalities (0.1) ||f(2x-y)+f(y-x)-f(x)|| $\leq$ ||${\rho}(f(x+y)-f(x)-f(y))$||, where ρ is a fixed complex number with |ρ| < 1, and (0.2) ||f(x+y)-f(x)-f(y)|| $\leq$ ||${\rho}(f(2x-y)-f(y-x)-f(x))$||, where ρ is a fixed complex number with |ρ| < $\frac{1}{2}$. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in β-homogeneous F-spaces.
Keywords
Hyers-Ulam stability; β -homogeneous F-space; additive ρ -functional inequality;
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