Abstracts on Fixed Point Theory

Abstracts on Fixed Point Theory for 1995

Garcia-Falcet J., Jimenez-Melado A., Llorens-Fuster E., Isomorphically Expansive Mappings in $l_2$
Abstract: In the Hilbert space $l_2$ it is impossible to find a renorming $||.||$ for which become nonexpansive the well known fixed point free mappings by Kakutani, Baillon and others. One fixed point theorem is given also.
For more on this abstract please contact the authors via email at jesus.garcia@vm.ci.uv.es
Posted: December 18,1995.

Prus S., Some Estimates for the Normal Structure Coefficient in Banach Spaces
Abstract: Estimates for the normal structure coefficient $N(X)$ are obtained in the case where the modulus of convexity of $X$ is larger than the modulus of convexity of a right hexagon or $X$ is uniformly smooth.
For more on this abstract please contact the author via email at bsprus@golem.umcs.lublin.pl
Posted: December 18,1995.

Dominguez Benavides T., Some Fixed Point Theorems in Orlicz Sequence Spaces
Abstract: It is proved an existence theorem of fixed point for uniformly Lipschitz mappings in Orlicz sequence spaces and a result about the stability of the fixed point property for nonexpansive mappings in the same setting. As a tool for these purposes, a lower bound for the modulus of the uniform Opial property is obtained in these spaces.
For more on this abstract please contact the author via email at ayerbe@cica.es
Posted: December 18,1995.

Besbes M., Extension des Theoremes de Points Fixes de Maurey aux Fonctions a valeurs Vectorielles
Abstract: On donne deux extensions vectorielles des theoremes de points fixes de Maurey dans les sous espaces reflexifs de $L^1$ et dans $c_0$. En particulier, on montre que si $X$ est uniformement convexe alors les sous espaces reflexifs de $L^1(X)$ possedent la propriete du point fixe. Il en est de meme de l'espace $c_0(X)$. Notre methode permet aussi de simplifier les demonstrations originales dans le cas scalaire.
For more on this abstract please contact the author.
Posted: December 18,1995.

Lau A.T., Mah P.F., Ulger A., Fixed Point Property and Normal Structure for Banach spaces associated to Locally Compact Groups
Abstract: In this paper we investigate when various Banach spaces associated to a locally group $G$ have the fixed point property for nonexpansive mappings or normal structure. We give sufficient conditions and some necessary conditions about $G$ for the Fourier and Fourier-Stieltjes algebras to have the fixed point property. We also show that if a $C^{\ast}$-algebra $\cal U$ has the fixed point property then for any normal element $a$ of $\cal U$, the spectrum $\sigma(a)$ is countable and that the group $C^{\ast}$-algebra $C^{\ast}(G)$ has the weak normal structure if and only if $G$ is finite.
For more on this abstract please contact the authors via email at tlau@vega.math.ualberta.ca
Posted: December 18,1995.

Khamsi M.A., Swaminathan S., Normal Structure in James Spaces
Abstract: The main result is that a general James space $J(X)$, where $X$ is a Banach space with a Schauder basis which is spreading and 1-unconditional, has normal structure if the basis is uniformly monotone.
For more on this abstract please contact the authors via email at swami@cs.dal.ca. For the post-script file please click Here.
Posted: December 18,1995.

Sims B., Smyth M., On some Banach space properties sufficient for Weak Normal Structure and their permanence properties
Abstract: We consider Banach space properties that lie between conditions introduced by bynum and Landes. These properties depend on the metric behavior of weakly convergent sequences. We also investigate the permanence properties of these conditions.
For more on this abstract please contact the author via email at bsims@frey.newcastle.edu.au
Posted: December 18,1995.

Khamsi M.A., KKM and Ky Fan theorems in hyperconvex metric spaces
Abstract: In Hyperconvex metric spaces, we introduce Knaster-Kuratowski-Mazurkiewicz mappings (in short KKM-maps). Then we prove an analogue to Ky Fan fixed point theorem in hyperconvex metric spaces.
For more on this abstract please contact the author via email at mohamed@math.utep.edu. For the post-script file please click Here.
Posted: December 18,1995.

Dominguez Benavides T., Fixed Point Theorems for Uniformly Lipschitzian Mappings and Asymptotically Regular Mappings
Abstract: Let $C$ be a closed convex bounded subset of a Banach space $X$ and $T:C \rightarrow C$ a uniformly Lipschitzian mappings, i.e. there exists $k >0$ such that $||T^n(x) - T^n(y)|| \leq ||x-y||$ for every $x,y \in C$. We prove that $T$ has a fixed point if $$k < \frac{1 + \sqrt{1 + 4N(X)(\kappa_0(X) - 1)}{2}$$ where $N(X)$ is the normal structure coefficient of $X$ and $\kappa_0(X)$ is the Lifschitz characteristic of $X$. For Banach spaces, this result is a strict generalization of the ``classic'' Lifschitz theorem. We also prove a similar result for asymptotically regular mapping, improving previous fixed point theorems for this class of mappings.
For more on this abstract please contact the author via email at ayerbe@cica.es
Posted: December 18,1995.

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