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Stability of a quadratic functional equation in intuitionistic fuzzy normed spaces

박원길|배재형
대한수학회 (The Korean Mathematical Society)|2011.04|대한수학회논문집 (Communications of the KMS)|제26권 제2호|pp. 237-251

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참고문헌

키워드

stabilityintuitionistic fuzzy normed space
주제분류수학

초록

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+y,z+w)+f(x-y,z-w)=2f(x,z)+2f(y,w)in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-dimensional vector variable quadratic mapping implies the completeness of IFNS.

Abstract

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+y,z+w)+f(x-y,z-w)=2f(x,z)+2f(y,w)in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-dimensional vector variable quadratic mapping implies the completeness of IFNS.

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