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Fixed points of upper semicontinuous mappings in locally G-convex spaces

Published online by Cambridge University Press:  17 April 2009

George Xian-Zhi Yuan
George Xian-Zhi Yuan
Affiliation:
Department of Mathematics, The University of Queensland, Brisbabne Qld 4072, Australia e-mail: xzy@maths.uq.edu.au
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Abstract

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In this paper a new fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values is established in the setting of an abstract convex structure – called a locally G-convex space, which generalises usual convexity such as locally convex H-spaces, locally convex spaces (locally H-convex spaces), hyperconvex metric spaces and locally convex topological spaces. Our fixed point theorem includes corresponding Fan-Glicksberg type fixed point theorems in locally convex H-spaces, locally convex spaces, hyperconvex metric space and locally convex spaces in the existing literature as special cases.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 469 - 478
Copyright
Copyright © Australian Mathematical Society 1998

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