New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space

Shujia Chen; Shaoyuan Xu

doi:doi:10.11648/j.pamj.20140306.13

| Peer-Reviewed

New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space

Shujia Chen, Shaoyuan Xu

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 6)

Received: 2 November 2014 Accepted: 16 November 2014 Published: 19 November 2014

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Petryshyn's theorem and some results of the Reference [8] are extended to the condensing mappings satisfying the interior condition.

Published in	Pure and Applied Mathematics Journal (Volume 3, Issue 6)
DOI	10.11648/j.pamj.20140306.13
Page(s)	126-131
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Condensing Mappings, Interior Condition, Fixed Point, Banach Space

References

[1]	W. V. Petryshyn, Structure of the fixed points sets of k-set-contractions, Arch. Ration. Mach. Anal., 40 (1971/71), 312-318.
[2]	K. Deimling, Nonlinear functional analysis, Springer-Verlag, New York/Berlin, 1985.
[3]	A. Granas and J. Dugundji, Fixed point theory, Springer-Verlag, New York/Berlin, 2003.
[4]	E. Zeidler, Nonlinear functional analysis and its applications, Springer-Verlag, New York/Berlin, 1986.
[5]	R. D. Nussbaum, The fixed point index and fixed point theorems for k-set-contractions, Univ. of Chicago, Ph. D. thesis, 1969.
[6]	F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc., 74 (1968), 660-665.
[7]	J. M. Antonio and C.H. Morales, Fixed point theorems under the interior condition, Proc. Amer. Math. Soc., 134 (2006), 501-507.
[8]	Shaoyuan Xu and Chongjun Zhu, New Fixed Point Theorems of Condensing Map-pings Satisfying the Interior Condition in Banach spaces, Anal. Theory Appl. 26 (1) (2010),43-52.

Cite This Article

Plain Text BibTeX RIS

APA Style

Shujia Chen, Shaoyuan Xu. (2014). New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space. Pure and Applied Mathematics Journal, 3(6), 126-131. https://doi.org/10.11648/j.pamj.20140306.13

Copy | Download

ACS Style

Shujia Chen; Shaoyuan Xu. New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space. Pure Appl. Math. J. 2014, 3(6), 126-131. doi: 10.11648/j.pamj.20140306.13

Copy | Download

AMA Style

Shujia Chen, Shaoyuan Xu. New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space. Pure Appl Math J. 2014;3(6):126-131. doi: 10.11648/j.pamj.20140306.13

Copy | Download

@article{10.11648/j.pamj.20140306.13,
  author = {Shujia Chen and Shaoyuan Xu},
  title = {New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {6},
  pages = {126-131},
  doi = {10.11648/j.pamj.20140306.13},
  url = {https://doi.org/10.11648/j.pamj.20140306.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140306.13},
  abstract = {In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Petryshyn's theorem and some results of the Reference [8] are extended to the condensing mappings satisfying the interior condition.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space
AU  - Shujia Chen
AU  - Shaoyuan Xu
Y1  - 2014/11/19
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140306.13
DO  - 10.11648/j.pamj.20140306.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 126
EP  - 131
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140306.13
AB  - In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Petryshyn's theorem and some results of the Reference [8] are extended to the condensing mappings satisfying the interior condition.
VL  - 3
IS  - 6
ER  -

Copy | Download

Author Information

Shujia Chen

Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou, China
Shaoyuan Xu

Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou, China

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Shujia Chen, Shaoyuan Xu. (2014). New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space. Pure and Applied Mathematics Journal, 3(6), 126-131. https://doi.org/10.11648/j.pamj.20140306.13

Copy | Download

ACS Style

Shujia Chen; Shaoyuan Xu. New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space. Pure Appl. Math. J. 2014, 3(6), 126-131. doi: 10.11648/j.pamj.20140306.13

Copy | Download

AMA Style

Shujia Chen, Shaoyuan Xu. New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space. Pure Appl Math J. 2014;3(6):126-131. doi: 10.11648/j.pamj.20140306.13

Copy | Download

@article{10.11648/j.pamj.20140306.13,
  author = {Shujia Chen and Shaoyuan Xu},
  title = {New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {6},
  pages = {126-131},
  doi = {10.11648/j.pamj.20140306.13},
  url = {https://doi.org/10.11648/j.pamj.20140306.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140306.13},
  abstract = {In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Petryshyn's theorem and some results of the Reference [8] are extended to the condensing mappings satisfying the interior condition.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space
AU  - Shujia Chen
AU  - Shaoyuan Xu
Y1  - 2014/11/19
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140306.13
DO  - 10.11648/j.pamj.20140306.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 126
EP  - 131
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140306.13
AB  - In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Petryshyn's theorem and some results of the Reference [8] are extended to the condensing mappings satisfying the interior condition.
VL  - 3
IS  - 6
ER  -

Copy | Download