ADDITIVE ρ-FUNCTIONAL INEQUALITIES IN β-HOMOGENEOUS F-SPACES
Additive ρ-functional inequalities in β-homogeneous F-spaces
한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2016, v.23 no.3, pp.319-328
https://doi.org/10.7468/jksmeb.2016.23.3.319
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)
LEE, HARIN,
CHA, JAE YOUNG,
CHO, MIN WOO,
&
KWON, MYUNGJUN.
(2016). ADDITIVE ρ-FUNCTIONAL INEQUALITIES IN β-HOMOGENEOUS F-SPACES. 한국수학교육학회지시리즈B:순수및응용수학, 23(3), 319-328, https://doi.org/10.7468/jksmeb.2016.23.3.319
Abstract
In this paper, we solve the additive ρ-functional inequalities (0.1) ||f(2x-y)+f(y-x)-f(x)|| <TEX>$\leq$</TEX> ||<TEX>${\rho}(f(x+y)-f(x)-f(y))$</TEX>||, where ρ is a fixed complex number with |ρ| < 1, and (0.2) ||f(x+y)-f(x)-f(y)|| <TEX>$\leq$</TEX> ||<TEX>${\rho}(f(2x-y)-f(y-x)-f(x))$</TEX>||, where ρ is a fixed complex number with |ρ| < <TEX>$\frac{1}{2}$</TEX>. 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
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Hyers-Ulam stability,
β-homogeneous F-space,
additive ρ-functional inequality