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ISSN : 1226-0657

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Vol.23 No.3

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ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
LEE, JUNG RYE
SHIN, DONG YUN
YUN,, S. , LEE,, J. R. , & SHIN,, D. Y. (2016). ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(3), 247-263, https://doi.org/10.7468/jksmeb.2016.23.3.247

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 &#x3C1;-functional inequalities (0.1) <TEX>$N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$</TEX> where &#x3C1; is a fixed real number with |&#x3C1;| &#x3C; 1, and (0.2) <TEX>$N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$</TEX> where &#x3C1; is a fixed real number with |&#x3C1;| &#x3C; <TEX>$\frac{1}{2}$</TEX>.

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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