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
Summary
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
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