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

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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

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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), 2024. 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.

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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

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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

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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

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@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}
}

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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
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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  -

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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

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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

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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

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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