ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED 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.247-263

https://doi.org/10.7468/jksmeb.2016.23.3.247

YUN, SUNGSIK (DEPARTMENT OF FINANCIAL MATHEMATICS, HANSHIN UNIVERSITY)
LEE, JUNG RYE (DEPARTMENT OF MATHEMATICS, DAEJIN UNIVERSITY)
SHIN, DONG YUN (DEPARTMENT OF MATHEMATICS, UNIVERSITY OF SEOUL)

YUN, SUNGSIK, LEE, JUNG RYE, & SHIN, DONG YUN. (2016). ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES. 한국수학교육학회지시리즈B:순수및응용수학, 23(3), 247-263, https://doi.org/10.7468/jksmeb.2016.23.3.247

복사

Abstract

Let <TEX>$M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$</TEX>, <TEX>$M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$</TEX>. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) <TEX>$N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$</TEX> where ρ is a fixed real number with |ρ| < 1, and (0.2) <TEX>$N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$</TEX> where ρ is a fixed real number with |ρ| < <TEX>$\frac{1}{2}$</TEX>.

keywords: fuzzy Banach space, additive-quadratic ρ-functional inequality, Hyers-Ulam stability

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논문 상세

Vol.23 No.3

ADDITIVE-QUADRATIC &#x3C1;-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

Abstract

한국수학교육학회지시리즈B:순수및응용수학

ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES