Abstracts on Fixed Point Theory for 1998
Abstracts on Fixed Point Theory for 1998
- George Xian-Zhi Yuan,
A Generalization of Fan-Glicksberg Fixed Point Theorem.
Abstract: 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 convex $MC$-space which generalizes usual convexity as well
as other abstract convexity structures such as locally convex $H$-spaces,
l.c.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, l.c.spaces, hyperconvex metric space and locally convex spaces
in the existing literatures as special cases, which, in turn, leads
to answer the question of Kirk and Shin (Fixed point theorems in
hyperconvex metric spaces, Houston J. Math, Vol. 23(1997), p.175-187)
in the affirmatively.
For more on this abstract please contact the authors via email at
xzy@maths.uq.edu.au
Posted: March 23,1998.
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