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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.

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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 

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Correspondence to Ishak Altun.

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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.

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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

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

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