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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.24 No.3

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QUADRATIC (ρ1,ρ2)-FUNCTIONAL INEQUALITY IN FUZZY BANACH SPACES

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2017, v.24 no.3, pp.179-190
https://doi.org/10.7468/jksmeb.2017.24.3.179
Park, Junha
Jo, Younghun
Kim, Jaemin
Kim, Taekseung
Park,, J. , Jo,, Y. , Kim,, J. , & Kim,, T. (2017). QUADRATIC (ρ1,ρ2)-FUNCTIONAL INEQUALITY IN FUZZY BANACH SPACES. , 24(3), 179-190, https://doi.org/10.7468/jksmeb.2017.24.3.179

Abstract

In this paper, we introduce and solve the following quadratic (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality (0.1) <TEX>N(2f(x+y2)+2f(x−y2)−f(x)−f(y),t)≤min(N(ρ1(f(x+y)+f(x−y)−2f(x)−2f(y)),t),N(ρ2(4f(x+y2)+f(x−y)−2f(x)−2f(y)),t))

</TEX> in fuzzy normed spaces, where <TEX>${\rho}_1</TEX><TEX>$</TEX> and <TEX>${\rho}_2$</TEX> are fixed nonzero real numbers with <TEX>${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$</TEX> < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality (0.1) in fuzzy Banach spaces.

keywords
fuzzy Banach space, quadratic (<tex> ${\rho}_1$</tex>, <tex> ${\rho}_2$</tex>)-functional inequality, fixed point method, Hyers-Ulam stability

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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