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ON THE FUZZY STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS

신동윤|장선영|이정례
한국수학교육학회|2010.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제17권 제1호|pp. 65-80

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참고문헌

키워드

fuzzy Banach spacequadratic functional equationgeneralized Hyers-Ulamstability
주제분류수학

초록

In [17,18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equationin fuzzy Banach spaces have been in vestigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces:(0.1) f(x+y)+f(x-y) = 2f(x)+2f(y),(0.2) f(ax+by)+f(ax-by) = 2a2 f(x)+2b2 f(y)for nonzero real numbers a, b with a != ±1.

Abstract

In [17,18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equationin fuzzy Banach spaces have been in vestigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces:(0.1) f(x+y)+f(x-y) = 2f(x)+2f(y),(0.2) f(ax+by)+f(ax-by) = 2a2 f(x)+2b2 f(y)for nonzero real numbers a, b with a != ±1.

참고문헌 (36)

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