Skip to main content
  • Research Article
  • Open access
  • Published:

Fixed Points of Weakly Compatible Maps Satisfying a General Contractive Condition of Integral Type

Abstract

We prove a fixed point theorem for weakly compatible maps satisfying a general contractive condition of integral type.

[12345678910111213141516171819202122]

References

  1. 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  MATH  MathSciNet  Google Scholar 

  2. 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  MATH  MathSciNet  Google Scholar 

  3. Djoudi A, Aliouche A: Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type. Journal of Mathematical Analysis and Applications 2007,329(1):31–45. 10.1016/j.jmaa.2006.06.037

    Article  MATH  MathSciNet  Google Scholar 

  4. 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  MATH  MathSciNet  Google Scholar 

  5. Türkoğlu D, Altun I: A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying an implicit relation. to appear in Matemática Mexicana. Boletín. Tercera Serie

  6. 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  MATH  MathSciNet  Google Scholar 

  7. Suzuki T: Meir-Keeler contractions of integral type are still Meir-Keeler contractions. International Journal of Mathematics and Mathematical Sciences 2007, 2007: 6 pages.

    Article  Google Scholar 

  8. Sessa S: On a weak commutativity condition of mappings in fixed point considerations. Institut Mathématique. Publications. Nouvelle Série 1982, 32 (46): 149–153.

    MathSciNet  Google Scholar 

  9. Rhoades BE, Sessa S: Common fixed point theorems for three mappings under a weak commutativity condition. Indian Journal of Pure and Applied Mathematics 1986,17(1):47–57.

    MATH  MathSciNet  Google Scholar 

  10. Sessa S, Fisher B: Common fixed points of weakly commuting mappings. Bulletin of the Polish Academy of Sciences. Mathematics 1987,35(5–6):341–349.

    MATH  MathSciNet  Google Scholar 

  11. Singh SL, Ha KS, Cho YJ: Coincidence and fixed points of nonlinear hybrid contractions. International Journal of Mathematics and Mathematical Sciences 1989,12(2):247–256. 10.1155/S0161171289000281

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Jungck G: Compatible mappings and common fixed points. II. International Journal of Mathematics and Mathematical Sciences 1988,11(2):285–288. 10.1155/S0161171288000341

    Article  MATH  MathSciNet  Google Scholar 

  14. Jungck G, Rhoades BE: Fixed points for set valued functions without continuity. Indian Journal of Pure and Applied Mathematics 1998,29(3):227–238.

    MATH  MathSciNet  Google Scholar 

  15. 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  MATH  MathSciNet  Google Scholar 

  16. Türkoğlu D, Altun I, Fisher B: Fixed point theorem for sequences of maps. Demonstratio Mathematica 2005,38(2):461–468.

    MathSciNet  Google Scholar 

  17. Singh SL, Mishra SN: Remarks on Jachymski's fixed point theorems for compatible maps. Indian Journal of Pure and Applied Mathematics 1997,28(5):611–615.

    MATH  MathSciNet  Google Scholar 

  18. Ćirić LjB, Ume JS: Some common fixed point theorems for weakly compatible mappings. Journal of Mathematical Analysis and Applications 2006,314(2):488–499. 10.1016/j.jmaa.2005.04.007

    Article  MATH  MathSciNet  Google Scholar 

  19. Ahmed MA: Common fixed point theorems for weakly compatible mappings. The Rocky Mountain Journal of Mathematics 2003,33(4):1189–1203. 10.1216/rmjm/1181075457

    Article  MATH  MathSciNet  Google Scholar 

  20. Chugh R, Kumar S: Common fixed points for weakly compatible maps. Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2001,111(2):241–247. 10.1007/BF02829594

    Article  MATH  MathSciNet  Google Scholar 

  21. Popa V: A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation. Univerzitet u Nišu. Prirodno-Matematički Fakultet. Filomat 2005, (19):45–51.

    Google Scholar 

  22. Matkowski J: Fixed point theorems for mappings with a contractive iterate at a point. Proceedings of the American Mathematical Society 1977,62(2):344–348. 10.1090/S0002-9939-1977-0436113-5

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ishak Altun.

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

Altun, I., Türkoğlu, D. & Rhoades, B.E. Fixed Points of Weakly Compatible Maps Satisfying a General Contractive Condition of Integral Type. Fixed Point Theory Appl 2007, 017301 (2007). https://doi.org/10.1155/2007/17301

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/17301

Keywords