Metric fixed point theory for multivalued mappings

Hong-Kun Xu

  • 2000

Abstract

top
Some new and recent results on the fixed point theory of multivalued contractions and nonexpansive mappings are presented. Discussions concerning Reich's problem are included. Existence of fixed points for weakly inward contractions is proved. Local contractions are also discussed. The Kirk-Massa theorem is extended to inward multivalued nonexpansive mappings. Using an inequality characteristic of uniform convexity, another proof of Lim's theorem on weakly inward multivalued nonexpansive mappings in a uniformly convex Banach space is included. The fixed point set function of a random contraction is proved to be measurable. Lim's fixed point theorem for nonexpansive self-mappings in a uniformly convex Banach space is randomized. Also, the fixed point set function of a single-valued random nonexpansive mapping in a uniformly smooth Banach space is shown to be measurable.

How to cite

top

Hong-Kun Xu. Metric fixed point theory for multivalued mappings. 2000. <http://eudml.org/doc/285935>.

@book{Hong2000,
abstract = {Some new and recent results on the fixed point theory of multivalued contractions and nonexpansive mappings are presented. Discussions concerning Reich's problem are included. Existence of fixed points for weakly inward contractions is proved. Local contractions are also discussed. The Kirk-Massa theorem is extended to inward multivalued nonexpansive mappings. Using an inequality characteristic of uniform convexity, another proof of Lim's theorem on weakly inward multivalued nonexpansive mappings in a uniformly convex Banach space is included. The fixed point set function of a random contraction is proved to be measurable. Lim's fixed point theorem for nonexpansive self-mappings in a uniformly convex Banach space is randomized. Also, the fixed point set function of a single-valued random nonexpansive mapping in a uniformly smooth Banach space is shown to be measurable.},
author = {Hong-Kun Xu},
keywords = {fixed point theory; non-expansive and contractive set-valued mappings; Kirk-Massa theorem; Reich problem},
language = {eng},
title = {Metric fixed point theory for multivalued mappings},
url = {http://eudml.org/doc/285935},
year = {2000},
}

TY - BOOK
AU - Hong-Kun Xu
TI - Metric fixed point theory for multivalued mappings
PY - 2000
AB - Some new and recent results on the fixed point theory of multivalued contractions and nonexpansive mappings are presented. Discussions concerning Reich's problem are included. Existence of fixed points for weakly inward contractions is proved. Local contractions are also discussed. The Kirk-Massa theorem is extended to inward multivalued nonexpansive mappings. Using an inequality characteristic of uniform convexity, another proof of Lim's theorem on weakly inward multivalued nonexpansive mappings in a uniformly convex Banach space is included. The fixed point set function of a random contraction is proved to be measurable. Lim's fixed point theorem for nonexpansive self-mappings in a uniformly convex Banach space is randomized. Also, the fixed point set function of a single-valued random nonexpansive mapping in a uniformly smooth Banach space is shown to be measurable.
LA - eng
KW - fixed point theory; non-expansive and contractive set-valued mappings; Kirk-Massa theorem; Reich problem
UR - http://eudml.org/doc/285935
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.