Abstract

AbstractWe discuss fixed point properties of convex subsets of locally convex linear topological spaces. We derive equivalence among fixed point properties concerning several types of multivalued mappings.

Highlights

  • We present fundamental definitions related to multivalued mappings in order to fix our terminology

  • A multivalued mapping F : X Y from X to Y is a function which attains a nonempty subset of Y for each point x of X and the subset is denoted by Fx

  • For any subset B of Y, the upper inverse Fu B and the lower inverse Fl B are defined by Fu B {x ∈ X : Fx ⊂ B} and Fl B {x ∈ X : Fx ∩ B / ∅}, respectively

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Summary

Hidetoshi Komiya

We discuss fixed point properties of convex subsets of locally convex linear topological spaces. We derive equivalence among fixed point properties concerning several types of multivalued mappings

Introduction
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