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

김재민|조영훈|박준하|김택승
한국수학교육학회|2017.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제24권 제3호|pp. 179-190|DOI https://doi.org/10.7468/jksmeb.2017.24.3.179

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참고문헌

키워드

fuzzy Banach spaceHyers-Ulam stability.fixed point methodρ2)-functional inequalityquadratic (ρ1
주제분류수학

초록

In this paper, we introduce and solve the following quadratic (½1; ½2)- functional inequality N µ 2f ³x + y 2 ´ + 2f ³x ¡ y 2 ´ ¡ f(x) ¡ f(y); t ¶ (0.1) · min µ N (½1 (f(x + y) + f(x ¡ y) ¡ 2f(x) ¡ 2f(y)) ; t) ; N ³ ½2 ³ 4f ³x + y 2 ´ + f(x ¡ y) ¡ 2f(x) ¡ 2f(y) ´ ; t ´¶ in fuzzy normed spaces, where ½1 and ½2 are ¯xed nonzero real numbers with 1 4j½1j + 1 4j½2j < 1, and f(0) = 0. Using the ¯xed point method, we prove the Hyers-Ulam stability of the quadratic (½1; ½2)-functional inequality (0.1) in fuzzy Banach spaces.

Abstract

In this paper, we introduce and solve the following quadratic (½1; ½2)- functional inequality N µ 2f ³x + y 2 ´ + 2f ³x ¡ y 2 ´ ¡ f(x) ¡ f(y); t ¶ (0.1) · min µ N (½1 (f(x + y) + f(x ¡ y) ¡ 2f(x) ¡ 2f(y)) ; t) ; N ³ ½2 ³ 4f ³x + y 2 ´ + f(x ¡ y) ¡ 2f(x) ¡ 2f(y) ´ ; t ´¶ in fuzzy normed spaces, where ½1 and ½2 are ¯xed nonzero real numbers with 1 4j½1j + 1 4j½2j < 1, and f(0) = 0. Using the ¯xed point method, we prove the Hyers-Ulam stability of the quadratic (½1; ½2)-functional inequality (0.1) in fuzzy Banach spaces.

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