完備距離空間におけるシャウダーの不動点定理 chauders ixed oint.pdfVIP

1457 2005 241-246 241 Schauder’s Fixed Point Theorems in Complete Metric Spaces and Fuzzy Boundary Value Problems on an Infinite Interval (Seiji SAITO), (Hiroaki ISHII) (Graduate School of Information Science and Technology, Osaka University) E-mail : saito, ishii @ist.osaka-u.ac.jp Osaka, Japan, 565-0871 Abstract Aims of our study are follows: One is to prove that a complete metric space of fuzzy numbers becomes a Banach space under a condition that the metric has a homogeneous property. Another is to give sufficient conditions that a subset in the complete metric space and an into continuous mapping on the subset have at least one fixed point by applying Schauder’s fixed point theorem. Finally we discuss a sufficient conditions for the existence of solutions of fuzzy differential equations on an infinite interval with boundary conditions. 1 Complete Metric Space of Fuzzy Numbers Denote $I=[0,1]$ . The follow ing definition means that a fuzzy number can be identified with a membership function. Definition 1 Denote a set of fuzzy numbers with bounded supports and strict fuzzy convexity by $F $ $( $ : satisfying below (i) $ has a unique number $m such that $ $=1$ (normality); (ii) supp(fi) $=cl( is bounded in $ (bounded support); (iii) $ is strictly fuzzy convex on suPp(ii) as follows: