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Fixed points of compact approachable multimaps in topological vector spaces

✍ Scribed by In-Sook Kim

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
528 KB
Volume
14
Category
Article
ISSN
0893-9659

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✦ Synopsis

Applying the homotopy extension theorem for compact approachable vector fields with star-shaped values, we prove the existence of fixed points and eigenvalues of compact approachable multimaps in topological vector spaces. In particular, we give the Birkhoff-Kellogg Theorem for compact approachable multimaps with star-shaped values in normed spaces.

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## In this note, we first prove existence theorems for noncompact generalized quasivariational inequalities. As applications, two fixed point theorems for upper or lower semicontinuous multivalued mappings without compact domains are given in locally Hausdorff topological vector spaces. These resu