Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces

Daya Ram Sahu

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 4, page 653-666
  • ISSN: 0010-2628

Abstract

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We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study the existence of fixed points and the structure of fixed point sets of mappings of these classes in Banach spaces. Our results improve various celebrated results of fixed point theory in the context of demicontinuity.

How to cite

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Sahu, Daya Ram. "Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 653-666. <http://eudml.org/doc/249562>.

@article{Sahu2005,
abstract = {We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study the existence of fixed points and the structure of fixed point sets of mappings of these classes in Banach spaces. Our results improve various celebrated results of fixed point theory in the context of demicontinuity.},
author = {Sahu, Daya Ram},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {asymptotically nonexpansive mapping; Banach contraction principle; fixed point; Lipschitzian mapping; nearly Lipschitzian mapping; nearly asymptotically nonexpansive mapping; uniformly convex Banach space; asymptotically nonexpansive mapping; Banach contraction principle},
language = {eng},
number = {4},
pages = {653-666},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces},
url = {http://eudml.org/doc/249562},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Sahu, Daya Ram
TI - Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 653
EP - 666
AB - We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study the existence of fixed points and the structure of fixed point sets of mappings of these classes in Banach spaces. Our results improve various celebrated results of fixed point theory in the context of demicontinuity.
LA - eng
KW - asymptotically nonexpansive mapping; Banach contraction principle; fixed point; Lipschitzian mapping; nearly Lipschitzian mapping; nearly asymptotically nonexpansive mapping; uniformly convex Banach space; asymptotically nonexpansive mapping; Banach contraction principle
UR - http://eudml.org/doc/249562
ER -

References

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