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

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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: Hyers-Ulam stability, β-homogeneous F-space, additive ρ-functional inequality

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논문 상세

Vol.23 No.3

ADDITIVE &#x3C1;-FUNCTIONAL INEQUALITIES IN &#x3B2;-HOMOGENEOUS F-SPACES

Additive ρ-functional inequalities in β-homogeneous F-spaces

Abstract

한국수학교육학회지시리즈B:순수및응용수학

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