Skip to main content
Fixed Point Theory and Algorithms for Sciences and Engineering
Download PDF
  • Research Article
  • Open access
  • Published:

Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type

Fixed Point Theory and Applications volume 2007, Article number: 054101 (2007) Cite this article

An Erratum to this article was published on 11 November 2008

Abstract

We obtain several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps defined on a symmetric space satisfying a contractive condition of integral type. The results of this paper essentially contain every theorem on hybrid and multivalued self-maps of a metric space as a special case.

Erratum http://dx.doi.org/10.1155/2008/274793

[123456789101112131415161718192021]

References

  1. Sessa S: On a weak commutativity condition of mappings in fixed point considerations. Publications de l'Institut Mathématique 1982, 32(46): 149–153.

    MathSciNet  MATH  Google Scholar 

  2. Jungck G: Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences 1986,9(4):771–779. 10.1155/S0161171286000935

    Article  MathSciNet  MATH  Google Scholar 

  3. Jungck G: Common fixed points for noncontinuous nonself maps on nonmetric spaces. Far East Journal of Mathematical Sciences 1996,4(2):199–215.

    MathSciNet  MATH  Google Scholar 

  4. Jungck G, Rhoades BE: Fixed point theorems for occasionally weakly compatible mappings. Fixed Point Theory 2006,7(2):287–296.

    MathSciNet  MATH  Google Scholar 

  5. Branciari A: A fixed point theorem for mappings satisfying a general contractive condition of integral type. International Journal of Mathematics and Mathematical Sciences 2002,29(9):531–536. 10.1155/S0161171202007524

    Article  MathSciNet  MATH  Google Scholar 

  6. Rhoades BE: Two fixed-point theorems for mappings satisfying a general contractive condition of integral type. International Journal of Mathematics and Mathematical Sciences 2003,2003(63):4007–4013. 10.1155/S0161171203208024

    Article  MathSciNet  MATH  Google Scholar 

  7. Aliouche A: A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type. Journal of Mathematical Analysis and Applications 2006,322(2):796–802. 10.1016/j.jmaa.2005.09.068

    Article  MathSciNet  MATH  Google Scholar 

  8. Vijayaraju P, Rhoades BE, Mohanraj R: A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type. International Journal of Mathematics and Mathematical Sciences 2005,2005(15):2359–2364. 10.1155/IJMMS.2005.2359

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang X: Common fixed point theorems for some new generalized contractive type mappings. Journal of Mathematical Analysis and Applications 2007,333(2):780–786. 10.1016/j.jmaa.2006.11.028

    Article  MathSciNet  MATH  Google Scholar 

  10. Nadler SB Jr.: Multi-valued contraction mappings. Pacific Journal of Mathematics 1969, 30: 475–488.

    Article  MathSciNet  MATH  Google Scholar 

  11. Naidu SVR: Fixed points and coincidence points for multimaps with not necessarily bounded images. Fixed Point Theory and Applications 2004,2004(3):221–242. 10.1155/S1687182004308090

    Article  MathSciNet  MATH  Google Scholar 

  12. Singh SL, Mishra SN: Coincidences and fixed points of nonself hybrid contractions. Journal of Mathematical Analysis and Applications 2001,256(2):486–497. 10.1006/jmaa.2000.7301

    Article  MathSciNet  MATH  Google Scholar 

  13. Dube LS: A theorem on common fixed points of multi-valued mappings. Annales de la Societé Scientifique de Bruxelles 1975,89(4):463–468.

    MathSciNet  MATH  Google Scholar 

  14. Azam A, Beg I: Coincidence points of compatible multivalued mappings. Demonstratio Mathematica 1996,29(1):17–22.

    MathSciNet  MATH  Google Scholar 

  15. Kamran T: Common coincidence points of -weakly commuting maps. International Journal of Mathematics and Mathematical Sciences 2001,26(3):179–182. 10.1155/S0161171201005245

    Article  MathSciNet  MATH  Google Scholar 

  16. Hadžić O: Common fixed point theorems for single-valued and multivalued mappings. Review of Research. Faculty of Science. Mathematics Series 1988,18(2):145–151.

    MathSciNet  MATH  Google Scholar 

  17. Kaneko H, Sessa S: Fixed point theorems for compatible multi-valued and single-valued mappings. International Journal of Mathematics and Mathematical Sciences 1989,12(2):257–262. 10.1155/S0161171289000293

    Article  MathSciNet  MATH  Google Scholar 

  18. Kaneko H: A common fixed point of weakly commuting multi-valued mappings. Mathematica Japonica 1988,33(5):741–744.

    MathSciNet  MATH  Google Scholar 

  19. Chang TH: Common fixed point theorems for multivalued mappings. Mathematica Japonica 1995,41(2):311–320.

    MathSciNet  MATH  Google Scholar 

  20. Shrivastava PK, Bawa NPS, Nigam SK: Fixed point theorems for hybrid contractions. Varāhmihir Journal of Mathematical Sciences 2002,2(2):275–281.

    MathSciNet  MATH  Google Scholar 

  21. Taylor LE: A contractive mapping without fixed points. Notices of the American Mathematical Society 1977, 24: A-649.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN, 47405-7106, USA

    Mujahid Abbas & BE Rhoades

  2. Department of Mathematics, Lahore University of Management Sciences, Lahore, 54792, Pakistan

    Mujahid Abbas

Authors
  1. Mujahid Abbas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. BE Rhoades
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to BE Rhoades.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1155/2008/274793.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Abbas, M., Rhoades, B. Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type. Fixed Point Theory Appl 2007, 054101 (2007). https://doi.org/10.1155/2007/54101

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/54101

Keywords