scholarly journals Nonexpansive Mappings in Locally Convex Spaces

1977 ◽  
Vol 20 (4) ◽  
pp. 455-461
Author(s):  
Troy L. Hicks ◽  
John D. Kubicek
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Point Property ◽  
Fixed Point Set ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
Locally Convex

Recently Bruck initiated the study of the structure of the fixed-point set of a nonexpansive selfmap T of a Banach space, where T satisfies a conditional fixed point property. We generalize many of his results to a Hausdorff locally convex space X. Also, we generalize a result of Holmes and Narayanaswami and use it, along with a procedure of Kiang, to obtain a fixed point theorem for families of asymptotically nonexpansive mappings in X.

scholarly journals The fixed-point property in Banach spaces containing a copy ofc0

2003 ◽  
Vol 2003 (3) ◽  
pp. 183-192
Author(s):  
Maria A. Japón Pineda
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Weak Topology ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Asymptotically Nonexpansive ◽  
Locally Convex Topology ◽  
Locally Convex

We prove that every Banach space containing an isomorphic copy ofc0fails to have the fixed-point property for asymptotically nonexpansive mappings with respect to some locally convex topology which is coarser than the weak topology. If the copy ofc0is asymptotically isometric, this result can be improved, because we can prove the failure of the fixed-point property for nonexpansive mappings.

scholarly journals Modified Hybrid Block Iterative Algorithm for Uniformly Quasi--Asymptotically Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Qiansheng Feng ◽  
Yongfu Su ◽  
Fangfang Yan
Keyword(s):  
Banach Space ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Fixed Point Set ◽  
Convergence Theorems ◽  
Uniformly Smooth ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

Saewan and Kumam (2010) have proved the convergence theorems for finding the set of solutions of a general equilibrium problems and the common fixed point set of a family of closed and uniformly quasi--asymptotically nonexpansive mappings in a uniformly smooth and strictly convex Banach spaceEwith Kadec-Klee property. In this paper, authors prove the convergence theorems and do not need the Kadec-Klee property of Banach space and some other conditions used in the paper of S. Saewan and P. Kumam. Therefore, the results presented in this paper improve and extend some recent results.

scholarly journals Fixed points and their approximations for asymptotically nonexpansive mappings in locally convex spaces

1995 ◽  
Vol 18 (2) ◽  
pp. 293-298 ◽  
Author(s):  
P. Vijayaraju
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Locally Convex Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Locally Convex ◽  
Convex Spaces

We construct an example that the class of asymptotically nonexpansive mappings include properly the class of nonexpansive mappings in locally convex spaces, prove a theorem on the existence of fixed points, and the convergence of the sequence of iterates to a fixed point for asymptotically nonexpansive mappings in locally convex spaces.

scholarly journals A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-25
Author(s):  
Rattanaporn Wangkeeree ◽  
Uthai Kamraksa ◽  
Rabian Wangkeeree
Keyword(s):  
Fixed Point ◽  
General Equilibrium ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Strictly Pseudocontractive Mapping ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

We introduce a general composite algorithm for finding a common element of the set of solutions of a general equilibrium problem and the common fixed point set of a finite family of asymptotically nonexpansive mappings in the framework of Hilbert spaces. Strong convergence of such iterative scheme is obtained which solving some variational inequalities for a strongly monotone and strictly pseudocontractive mapping. Our results extend the corresponding recent results of Yao and Liou (2010).

scholarly journals Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings

2019 ◽  
Vol 20 (1) ◽  
pp. 119
Author(s):  
M. Radhakrishnan ◽  
S. Rajesh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Uniformly Convex ◽  
Point Property ◽  
Opial Condition ◽  
Nonexpansive Maps ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

<p>Kirk introduced the notion of pointwise eventually asymptotically non-expansive mappings and proved that uniformly convex Banach spaces have the fixed point property for pointwise eventually asymptotically non expansive maps. Further, Kirk raised the following question: “Does a Banach space X have the fixed point property for pointwise eventually asymptotically nonexpansive mappings when ever X has the fixed point property for nonexpansive mappings?”. In this paper, we prove that a Banach space X has the fixed point property for pointwise eventually asymptotically nonexpansive maps if X  has uniform normal structure or X is uniformly convex in every direction with the Maluta constant D(X) &lt; 1. Also, we study the asymptotic behavior of the sequence {T<sup>n</sup>x} for a pointwise eventually asymptotically nonexpansive map T defined on a nonempty weakly compact convex subset K of a Banach space X whenever X satisfies the uniform Opial condition or X has a weakly continuous duality map.</p>

scholarly journals Fixed point theorems for a sum of two mappings in locally convex spaces

1994 ◽  
Vol 17 (4) ◽  
pp. 681-686 ◽  
Author(s):  
P. Vijayaraju
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Locally Convex Spaces ◽  
Continuous Mappings ◽  
Asymptotically Nonexpansive ◽  
Locally Convex ◽  
Convex Spaces

Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. In this paper, we prove by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces. These results extend a result of Cain and Nashed.

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

scholarly journals Towards the fixed point property for superreflexive spaces

2001 ◽  
Vol 64 (3) ◽  
pp. 435-444 ◽  
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unit Sphere ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Geometrical Condition

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

Sign in / Sign up

Export Citation Format

Share Document