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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 580297, 5 pages
http://dx.doi.org/10.1155/2014/580297
Research Article

A Generalization of a Greguš Fixed Point Theorem in Metric Spaces

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Pure Mathematics, University of Shahrekord, Shahrekord 88186-34141, Iran
3School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746, Iran

Received 30 January 2014; Accepted 22 February 2014; Published 25 March 2014

Academic Editor: Giuseppe Marino

Copyright © 2014 Marwan A. Kutbi et al. 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. M. Greguš, “A fixed point theorem in Banach space,” Bollettino della Unione Matematica Italiana A, vol. 5, pp. 193–198, 1980. View at Google Scholar
  2. B. Fisher and S. Sessa, “On a fixed point theorem of Greguš,” International Journal of Mathematics and Mathematical Sciences, vol. 9, pp. 23–28, 1986. View at Google Scholar
  3. G. Jungck, “On a fixed point theorem of Fisher and Sessa,” International Journal of Mathematics and Mathematical Sciences, vol. 13, pp. 497–500, 1990. View at Google Scholar
  4. N. Hussain, B. E. Rhoades, and G. Jungck, “Common fixed point and invariant approximation results for Greguš type I-contractions,” Numerical Functional Analysis and Optimization, vol. 28, no. 9-10, pp. 1139–1151, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Aliouche, “Common fixed point theorems of Gregšs type for weakly compatible mappings satisfying generalized contractive conditions,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 707–719, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. V. Berinde, “Some remarks on a fixed point theorem for Ćirić-type almost contractions,” Carpathian Journal of Mathematics, vol. 25, no. 2, pp. 157–162, 2009. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. L. B. Ćirić, “On some discontinuous fixed point mappings in convex metric spaces,” Czechoslovak Mathematical Journal, vol. 43, no. 118, pp. 319–326, 1993. View at Google Scholar · View at Zentralblatt MATH
  8. L. B. Ćirić, “On a generalization of a Greguš fixed point theorem,” Czechoslovak Mathematical Journal, vol. 50, no. 125, pp. 449–458, 2000. View at Google Scholar
  9. L. B. Ćirić, “On a common fixed point theorem of a Greguš type,” Publications de l'Institut Mathématique, vol. 49, no. 63, pp. 174–178, 1991. View at Google Scholar
  10. L. B. Ćirić, “Generalized contractions and fixed-point theorems,” Publications de l'Institut Mathématique, vol. 12, pp. 19–26, 1971. View at Google Scholar · View at Zentralblatt MATH
  11. 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
  12. B. Fisher, “Common fixed points on a Banach space,” Chung Yuan, vol. 11, pp. 19–26, 1982. View at Google Scholar
  13. R. Herman and E. R. Jean, Equivalents of the Axiom of Choice, North-Holland, Amsterdam, The Netherlands, 1970.
  14. N. J. Huang and Y. J. Cho, “Common fixed point theorems of Greguš type in convex metric spaces,” Japanese Mathematics, vol. 48, pp. 83–89, 1998. View at Google Scholar
  15. N. Hussain, “Common fixed points in best approximation for Banach operator pairs with Ćirić type I-contractions,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1351–1363, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. Y. J. Cho and N. Hussain, “Weak contractions, common fixed points, and invariant approximations,” Journal of Inequalities and Applications, vol. 2009, Article ID 390634, 10 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. G. Jungck and N. Hussain, “Compatible maps and invariant approximations,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1003–1012, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. L. Bing-you, “Fixed point theorem of nonexpansive mappings in convex metric spaces,” Applied Mathematics and Mechanics, vol. 10, no. 2, pp. 183–188, 1989. View at Publisher · View at Google Scholar · View at Scopus
  19. R. N. Mukherjea and V. Verma, “A note on a fixed point theorem of Greguš,” Japanese Journal of Mathematics, vol. 33, pp. 745–749, 1988. View at Google Scholar
  20. P. P. Murthy, Y. J. Cho, and B. Fisher, “Common fixed points of Greguš type mappings,” Glasnik Matematicki, no. 50, pp. 335–341, 1995. View at Google Scholar
  21. S. Moradi and A. Farajzadeh, “On Olaleru's open problem on Greguš fixed point theorem,” Journal of Global Optimization, vol. 56, no. 4, pp. 1689–1697, 2013. View at Google Scholar
  22. R. H. Haghi, S. Rezapour, and N. Shahzad, “Some fixed point generalizations are not real generalizations,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 5, pp. 1799–1803, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. H. Fukhar-ud-din, A. R. Khan, and Z. Akhtar, “Fixed point results for a generalized nonexpansive map in uniformly convex metric spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 75, pp. 4747–4760, 2012. View at Publisher · View at Google Scholar · View at Scopus