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

ISSN : 3059-0604

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Vol.27 No.1

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

Quadratic(ρ1, p2)-functional Equation in Fuzzy Banach Spaces

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2020, v.27 no.1, pp.25-33
https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.1.25
Paokant, Siriluk (Department of Mathematics, Research Institute for Natural Sciences, Hanyang University)
Shin, Dong Yun (Department of Mathematics, University of Seoul)
Paokant, Siriluk, & Shin, Dong Yun. (2020). QUADRATIC (&#961;<sub>1</sub>, &#961;<sub>2</sub>)-FUNCTIONAL EQUATION IN FUZZY BANACH SPACES, 27(1), 25-33, https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.1.25

Abstract

In this paper, we consider the following quadratic (ρ1, ρ2)-functional equation (0, 1) $$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$, where ρ2 are fixed nonzero real numbers with ρ2 ≠ 1 and 2ρ1 + 2ρ2≠ 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ1, ρ2)-functional equation (0.1) in fuzzy Banach spaces.

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

한국수학교육학회지시리즈B:순수및응용수학

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