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Báo cáo hóa học: " FIXED POINT THEOREMS IN GENERATING SPACES OF QUASI-NORM FAMILY AND APPLICATIONS "

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: FIXED POINT THEOREMS IN GENERATING SPACES OF QUASI-NORM FAMILY AND APPLICATIONS | FIXED POINT THEOREMS IN GENERATING SPACES OF QUASI-NORM FAMILY AND APPLICATIONS JIAN-ZHONG XIAO AND XING-HUA ZHU Received 11 April 2005 Accepted 21 November 2005 Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces several Schauder-type fixed point theorems are proved which include the corresponding theorems in locally convex spaces as their special cases. As applications some new fixed point theorems in Menger probabilistic normed spaces and fuzzy normed spaces are obtained. Copyright 2006 J.-Z. Xiao and X.-H. Zhu. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The Schauder fixed point theorem and its generalizations which were obtained by Kras-noselskii et al. see 3 5 we call them the Schauder-type fixed point theorems play important role in nonlinear analysis. In classical case many interesting extensions and important applications of these theorems were presented by Fan 1 and others. In non-classical case several extensions of these theorems in Menger probabilistic normed spaces were given under some conditions by Zhang-Guo 11 and Lin 6 . Naturally a subject is to consider their unified extensions both in classical case and in nonclassical case. In this paper we introduce some new concepts of generating spaces of quasi-norm family and establish some new unified versions of Schauder-type fixed point theorems in more general setting. As applications we also study the existence problems concerning the fixed points for operators on Menger probabilistic normed space and fuzzy normed space. Our results contain not only the former versions of the Schauder-type fixed point theorems but also the corresponding theorems in Menger