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Continuous selection theorem, coincidence theorem and intersection theorems concerning sets with H-convex sections

Part of: Connections with other structures, applications General convexity Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  09 April 2009

Xie-Ping Ding
Xie-Ping Ding
Affiliation:
Sichuan Normal University Chengdu, Sichuan People's, Republic of China
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Abstract

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A continuous selection and a coincidence theorem are proved in H-spaces which generalize the corresponding results of Ben-El-Mechaiekh-Deguire-Granas, Browder, Ko-Tan, Lassonde, Park, Simon and Takahashi to noncompact and/or nonconvex settings. By applying the two theorems, some intersection theorems concerning sets with H-convex sections are obtained which generalize the corresponding results of Fan, Lassonde and Shih-Tan to H-spaces. Some applications to minimax principle are given.

Keywords

Continuous selectioncoincidenceH-spacecontractibleweakly H-convexH – KKMcompactly closed (open)upper semi-continuousminimεx principle

MSC classification

Secondary: 54C65: Selections 54H25: Fixed-point and coincidence theorems 52A07: Convex sets in topological vector spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 1 , February 1992 , pp. 11 - 25
Copyright
Copyright © Australian Mathematical Society 1992

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