• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.93-104
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• 2021

In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadžić type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-264
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• 1995

Applications of the classical Knaster-Kuratowski-Mazurkiewicz (si-mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [L1]. In this direction, the first author [P5] found that certain coincidence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory.