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Fixed Point Theorem in Cone Metric Space

Received: 19 December 2016     Accepted: 24 January 2017     Published: 22 February 2017
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Abstract

In this paper, we prove a unique common fixed point theorem for four self-mappings in cone metric spaces by using the continuity and commuting mappings. Our result extends,improvesthe results of [M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341(2008) 416-420].

Published in International Journal of Discrete Mathematics (Volume 2, Issue 1)
DOI 10.11648/j.dmath.20170201.14
Page(s) 17-19
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), 2017. Published by Science Publishing Group

Keywords

Cone Metric Space, Fixed Point, Common Fixed Point

References
[1] M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341(2008) 416-420.
[2] M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 21(2008)511-515.
[3] I. Altun, B. Damnjanovic, D. Djoric, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett. (2009) doi:10.1016/j.aml.2009.09.016.
[4] M. Amari, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270(2002)181-188.
[5] M. Arshad, A. Azam, P. Vetro, Some common fixed point results on cone metric spaces, Fixed Point Theory Appl. (2009) 11, Article ID 493965.
[6] Guangxing Song, Xiaoyan Sun, Yian Zhao, Guotao Wang, New common fixed point theorems for maps on cone metric spaces, Appl. Math. Lett. 32(2010)1033-1037.
[7] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332(2) (2007)1468-1476.
[8] D. IIic, V. Rakocevic, Common fixed points for maps on cone metric space, J. Math. Anal. Appl. 341(2008) 876-886.
[9] S. Radenović, B. E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces, Comput. Math. Appl. 57 (2009) 1701–1707.
[10] Sh. Rezapour and R. Hamlbarani, Some notes on the paper cone metric spaces and fixed point theorem of contractive mappings, J. Math. Anal. Appl. 345(2008), 719-724.
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  • APA Style

    K. Prudhvi. (2017). Fixed Point Theorem in Cone Metric Space. International Journal of Discrete Mathematics, 2(1), 17-19. https://doi.org/10.11648/j.dmath.20170201.14

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    ACS Style

    K. Prudhvi. Fixed Point Theorem in Cone Metric Space. Int. J. Discrete Math. 2017, 2(1), 17-19. doi: 10.11648/j.dmath.20170201.14

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    AMA Style

    K. Prudhvi. Fixed Point Theorem in Cone Metric Space. Int J Discrete Math. 2017;2(1):17-19. doi: 10.11648/j.dmath.20170201.14

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  • @article{10.11648/j.dmath.20170201.14,
      author = {K. Prudhvi},
      title = {Fixed Point Theorem in Cone Metric Space},
      journal = {International Journal of Discrete Mathematics},
      volume = {2},
      number = {1},
      pages = {17-19},
      doi = {10.11648/j.dmath.20170201.14},
      url = {https://doi.org/10.11648/j.dmath.20170201.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170201.14},
      abstract = {In this paper, we prove a unique common fixed point theorem for four self-mappings in cone metric spaces by using the continuity and commuting mappings. Our result extends,improvesthe results of [M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341(2008) 416-420].},
     year = {2017}
    }
    

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    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
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    AB  - In this paper, we prove a unique common fixed point theorem for four self-mappings in cone metric spaces by using the continuity and commuting mappings. Our result extends,improvesthe results of [M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341(2008) 416-420].
    VL  - 2
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Author Information
  • Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, India

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