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

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

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 (ρ1, ρ2)-FUNCTIONAL EQUATION IN FUZZY BANACH SPACES. 한국수학교육학회지시리즈B:순수및응용수학, 27(1), 25-33, https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.1.25

복사

Abstract

In this paper, we consider the following quadratic (ρ1, ρ2)-functional equation (0, 1) <TEX>$$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$</TEX>, 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

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학

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QUADRATIC (&#961;<sub>1</sub>, &#961;<sub>2</sub>)-FUNCTIONAL EQUATION IN FUZZY BANACH SPACES

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Abstract

한국수학교육학회지시리즈B:순수및응용수학

QUADRATIC (ρ<sub>1</sub>, ρ<sub>2</sub>)-FUNCTIONAL EQUATION IN FUZZY BANACH SPACES