Recent Abstracts on Fixed Point Theory
Abstracts on Fixed Point Theory for 1996
- Xu H-K,, Geometrical coefficients of Banach spaces and
nonlinear mappings
Abstract: Some geometrical coefficients of Banach spaces and their
role in fixed point theory of nonlinear mappings are discussed. The
uniform Opial property and Opial's modulus are concerned. The
demiclosedness principle and asymptotic behavior for mappings of
asymptotically nonexpansive type are studied. An existence result of
fixed points for this type of mappings is proved.
For more on this abstract please contact the author via email at
hkxu@pixie.udw.ac.za
Posted: February 5,1996.
- Sims B. , Banach space geometry and the fixed point
property(For a Post-Script version of this paper Click
Here)
Abstract: This is the text of four lectures given at the special
international
workshop on metric fixed point theory held at the
University of Seville from September 25 -- 29, 1995. I would
like to thank the University of Seville and the Workshop organizers
for the invitation to participate in the workshop and for their
efforts to stage such a rewarding and scientifically successful
meeting.
For more on this abstract please contact the author via email at
bsims@frey.newcastle.edu.au
Posted: February 6,1996.
- Seda A.K., Quasi-metrics and the Semantics of Logic
Programs
Abstract: Quasi-metrics have been used in several places in the
literature on domain theory and the formal semantics of programming
languages. In this paper, we consider the role of quasi-metrics in
the fixed point semantics of logic programs, examining in detaila
quite general process by which fixed points of immediate consequence
operators can be found. This work takes as its starting point:
(i)Fitting's recent application of the Banach contraction mapping
theorem in logic programming; (ii) a theorem of Rutten which
generalises both the contraction mapping theorem and the
Knaster-Tarski theorem; (iii) Smyth's work on totally bounded spaces
and compact ordered spaces as domains of computation. Our results
therefore are theoretical and to be viewed as a contribution to the
mathematical foundations of computer science.
For more on this abstract please contact the author via email at
aks@bureau.ucc.ie
Posted: March 6,1996.
- Kirk W.A., Shin S.S., Fixed Point Theorems in
Hyperconvex Spaces
Abstract: A number of new fixed poimt theorems are proved for
mappings in hyperconvex metric spaces. Crucial to the approach is the
relationship between hyperconvex metric spaces and nonexpansive
retractions and extensions.
For more on this abstract please contact the author via email at
william-kirk@uiowa.edu
Posted: March 6,1996.
- Nguyen T.N., Sanjurjo J.M.R., Tran V.A., The
AR-Property for Robert's example of a compact convex set with no
extreme points (Part 1 and Part 2)
Abstract: We prove that the original compact convex set with no
extreme points, constructed by Roberts, is an absolute retract,
therefore is homeomorphic to the Hilbert cube. Our proof consists of
two parts. In the first part, we give a sufficient condition for a
Roberts space to be an AR. In the second part of the paper, we apply
this to show that the example of Roberts is an AR.
For more on this abstract please contact the author via email at
nhnguyen@indiana.edu
Posted: March 6,1996.
- Nguyen T.N. , The fixed point property for weakly
admissible compact convex sets: searching for a solution to Schauder's
conjecture
Abstract: A compact convex set $X$ in a linear metric space is
weakly admissoble if for every $\epsilon > 0$ there exist compact
convex subsets $X_1,X_2,..,X_n$ of $X$ with $X = conv(X_1\cup X_2\cup
..\cup X_n)$ and continuous maps $f_i$ from $X_i$ into finite
dimensional subsets $E_i$, ($i=1,2,..,n$), of $X$ such that
$\sum ||f_i(x_i) - x_i|| < \epsilon$ for every $x_i \in X_i$.
Theorem: Any weakly admissible compact convex set has the fixed
point property.
Question: Is every weakly admissible compact convex set an AR?
For more on this abstract please contact the author via email at
nhnguyen@indiana.edu
Posted: March 6,1996.
- Kirk W.A., Sims B. , Nonlinear Isometries in
Superreflexive spaces
Abstract: We extend Maurey's theorem on the existence of a fixed
point for an isometry of a nonempty closed bounded convex subset of a
superreflexive space to obtain the existence of common fixed points
for countable families of commuting isometries.
For more on this abstract please contact the authors via email at
bsims@frey.newcastle.edu.au
Posted: March 26,1996.
- Kirk W.A., Conitnuous Mappings in Compact Hyperconvex
Metric Spaces
Abstract: A constructive fixed point theorem which arises in
interval analysis is extended to compact hyperconvex metric spaces.
For more on this abstract please contact the author via email at
william-kirk@uiowa.edu
Posted: June 5,1996.
- J. Jaworowski, N.T. Nguyen, P. Sisson, Rigid Spaces and the AR-Property
Abstract: A rigid space is a topological vector space whose
endomorphisms are all simply scalar multiples of the identity. A
rigid space can be constructed to admit compact operators. This paper
proves that the rigid space admitting compact operators constructed
by Sisson in one of his earlier papers (Studia Math 1995) is an AR,
hence is homeomorphic to the Hilbert space $l_2$.
For more on this abstract please contact the author via email at
nhnguyen@indiana.edu
Posted: October 4,1996.
- Jimenez-Melado A., Llorens-Fuster E.,
Opial Modulus and Stability of the Fixed Point Property(For a DVI version of this paper Click
Here)
Abstract: Our main result shows that a Banach space $Y$ has the fixed point
property whenever the Banach-Mazur distance from $Y$ to a Hilbert space is
less than $\sqrt{ 2+\sqrt{2}}$.
For more on this abstract please contact the authors via email at
llorens@uv.es
Posted: October 25,1996.
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