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  • P-ISSN1226-0657
  • E-ISSN2287-6081
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ISSN : 1226-0657

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Vol.23 No.2

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Additive-quadratic -functional inequalities in fuzzy Banach 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.2, pp.163-179
https://doi.org/10.7468/jksmeb.2016.23.2.163
LEE, SUNG JIN
SEO, JEONG PIL
LEE,, S. J. , & SEO,, J. P. (2016). Additive-quadratic -functional inequalities in fuzzy Banach spaces. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(2), 163-179, https://doi.org/10.7468/jksmeb.2016.23.2.163

Abstract

Let <TEX>$M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$</TEX>, <TEX>$M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$</TEX> Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic &#x3C1;-functional inequalities (0.1) <TEX>$N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$</TEX> and (0.2) <TEX>$N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$</TEX> in fuzzy Banach spaces, where &#x3C1; is a fixed real number with &#x3C1; &#x2260; 1.

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

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