Open Access

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

Fixed Point Theory and Applications20072007:017301

DOI: 10.1155/2007/17301

Received: 10 October 2006

Accepted: 14 September 2007

Published: 25 October 2007

Abstract

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

[12345678910111213141516171819202122]

Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Science and Arts, Kirikkale University, Yahsihan
(2)
Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar
(3)
Department of Mathematics, Indiana University

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/S0161171202007524MATHMathSciNetView ArticleGoogle 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.2005.09.068MATHMathSciNetView ArticleGoogle 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.2006.06.037MATHMathSciNetView ArticleGoogle 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/S0161171203208024MATHMathSciNetView ArticleGoogle 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.2005.2359MATHMathSciNetView ArticleGoogle 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.View ArticleGoogle 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.MathSciNetGoogle 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.MATHMathSciNetGoogle 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.MATHMathSciNetGoogle 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/S0161171289000281MATHMathSciNetView ArticleGoogle Scholar
  12. Jungck G: Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences 1986,9(4):771–779. 10.1155/S0161171286000935MATHMathSciNetView ArticleGoogle 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/S0161171288000341MATHMathSciNetView ArticleGoogle 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.MATHMathSciNetGoogle 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/S0161171289000293MATHMathSciNetView ArticleGoogle Scholar
  16. Türkoğlu D, Altun I, Fisher B: Fixed point theorem for sequences of maps. Demonstratio Mathematica 2005,38(2):461–468.MathSciNetGoogle 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.MATHMathSciNetGoogle 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.2005.04.007MATHMathSciNetView ArticleGoogle 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/1181075457MATHMathSciNetView ArticleGoogle 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/BF02829594MATHMathSciNetView ArticleGoogle 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/S0002-9939-1977-0436113-5MATHMathSciNetView ArticleGoogle Scholar

Copyright

© Ishak Altun et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.