Table of Contents
Journal of Operators
Volume 2015 (2015), Article ID 195731, 9 pages
http://dx.doi.org/10.1155/2015/195731
Research Article

Common Fixed Point Theorems of Greguš Type -Weak Contraction for -Weakly Commuting Mappings in 2-Metric Spaces

Department of Pure and Applied Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh 495009, India

Received 14 July 2015; Accepted 21 September 2015

Academic Editor: Ram U. Verma

Copyright © 2015 Penumarthy Parvateesam Murthy and Uma Devi Patel. 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.

Linked References

  1. Y. I. Alber and S. Guerre-Delabriere, “Principle of weakly contractive maps in Hilbert spaces,” in New Results in Operator Theory and Its Applications, I. Gohberg and Y. Lyubich, Eds., vol. 98 of Operator Theory: Advances and Applications, pp. 7–22, Birkhäuser, Basel, Switzerland, 1997. View at Google Scholar
  2. B. E. Rhoades, “Some theorems on weakly contractive maps,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 4, pp. 2683–2693, 2001. View at Publisher · View at Google Scholar
  3. P. N. Dutta and B. S. Choudhury, “A generalisation of contraction principle in metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 406368, 8 pages, 2008. View at Publisher · View at Google Scholar
  4. Q. Zhang and Y. Song, “Common point theory for generalized φ-weak contractions,” Applied Mathematics Letters, vol. 22, no. 1, pp. 75–78, 2009. View at Publisher · View at Google Scholar
  5. D. Đorić, “Common fixed point for generalized (ψ,φ)-weak contractions,” Applied Mathematics Letters, vol. 22, no. 12, pp. 1896–1900, 2009. View at Publisher · View at Google Scholar
  6. S. Gahler, “2-Metrische Räume und ihre topologische structure,” Mathematische Nachrichten, vol. 26, pp. 115–148, 1963. View at Google Scholar
  7. S. Gahler, “Uber die unformesior bakat 2-metriche Reume,” Mathematische Nachrichten, vol. 28, pp. 235–244, 1965. View at Google Scholar
  8. S. Gähler, “Zur geometrie 2-metrischer Räume,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 11, pp. 665–667, 1966. View at Google Scholar
  9. B. C. Dhage, A study of some fixed points theorems [Ph.D. thesis], Marathawada University, Aurangabad, India, 1984.
  10. Z. Mustafa and B. Sims, “Some remarks concerning D-metric spaces,” in Proceedings of the International Conference on Fixed Point Theory and Applications, pp. 189–198, Valencla, Spain, July 2003.
  11. Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 7, no. 2, pp. 289–297, 2006. View at Google Scholar · View at MathSciNet
  12. S. V. R. Naidu and J. TR. Prasad, “Fixed point theoems in 2-metric spaces,” Indian Journal of Pure and Applied Mathematics, vol. 17, no. 8, pp. 974–993, 1988. View at Google Scholar · View at MathSciNet
  13. K. Iseki, “Fixed point theorems in 2-metric spaces,” Mathematics Seminar Notes, vol. 3, pp. 133–136, 1975. View at Google Scholar
  14. M. R. Singh, L. S. Singh, and P. P. Murthy, “Common fixed points of set valued mappings,” International Journal of Mathematics and Mathematical Sciences, vol. 25, no. 6, pp. 411–415, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. E. Abd EL-Monsef, H. M. Abu-Donia, and K. Abd-Rabou, “New types of common fixed point theorems in 2-metric spaces,” Chaos, Solitons and Fractals, vol. 41, no. 3, pp. 1435–1441, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. P. P. Murthy and K. Tas, “New common fixed point theorems of Greguš type for R-weakly commuting mappings in 2-metric spaces,” Hacettepe Journel of Mathematics and Statistics, vol. 38, no. 3, pp. 285–291, 2009. View at Google Scholar
  17. M. Greguš, “A fixed point theorem in Banach Spaces,” Bollettino dell'Unione Matematica Italiana A, vol. 17, pp. 193–198, 1980. View at Google Scholar
  18. M. L. Diviccaro, B. Fisher, and S. Sessa, “A common fixed point theorem of Greguš type,” Publicationes Mathematicae Debrecen, vol. 34, pp. 83–89, 1987. View at Google Scholar
  19. B. Fisher and S. Sessa, “On a fixed point theorem of Greguš,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 1, pp. 23–28, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  20. R. N. Mukherjee and V. Verma, “A note on a fixed point theorem of Greguš,” Mathematica Japonica, vol. 33, no. 5, pp. 745–749, 1988. View at Google Scholar · View at MathSciNet
  21. P. P. Murthy, Y. J. Cho, and B. Fisher, “Common fixed points of Greguš type mappings,” Glasnik Matematicki, vol. 30, no. 50, pp. 335–341, 1995. View at Google Scholar