Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 102980, 11 pages
http://dx.doi.org/10.1155/2012/102980
Research Article

Common Fixed Points, Invariant Approximation and Generalized Weak Contractions

Department of Mathematics, Khalsa College of Engineering & Technology (Punjab Technical University), Ranjit Avenue, Amritsar-143001, India

Received 23 March 2012; Revised 23 August 2012; Accepted 31 August 2012

Academic Editor: Harvinder S. Sidhu

Copyright © 2012 Sumit Chandok. 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. R. Kannan, “Some results on fixed points,” Bulletin of the Calcutta Mathematical Society, vol. 60, pp. 71–76, 1968. View at Google Scholar · View at Zentralblatt MATH
  2. R. Kannan, “Some results on fixed points. II,” The American Mathematical Monthly, vol. 76, pp. 405–408, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. S. K. Chatterjea, “Fixed-point theorems,” Comptes Rendus de l'Académie Bulgare des Sciences, vol. 25, pp. 727–730, 1972. View at Google Scholar · View at Zentralblatt MATH
  4. Ya. I. Alber and S. Guerre-Delabriere, “Principle of weakly contractive maps in Hilbert spaces,” in New Results in Operator Theory, I. Gohberg and Yu. Lyubich, Eds., vol. 8 of Operator Theory: Advances and Applications, pp. 7–22, Birkhäuser, Basel, Switzerland, 1997. View at Google Scholar · View at Zentralblatt MATH
  5. B. S. Choudhury, “Unique fixed point theorem for weakly C-contractive mappings,” Kathmandu University Journal of Science, Engineering and Technology, vol. 5, pp. 6–13, 2009. View at Google Scholar
  6. B. E. Rhoades, “Some theorems on weakly contractive maps,” Nonlinear Analysis, vol. 47, pp. 2683–2693, 2001. View at Google Scholar
  7. L. Ćirić, N. Hussain, and N. Cakić, “Common fixed points for Ćirić type f-contraction with applications,” Publicationes Mathematicae Debrecen, vol. 4317, pp. 1–19, 2009. View at Google Scholar
  8. S. Chandok, “Some common fixed point theorems for generalized f-weakly contractive mappings,” Journal of Applied Mathematics & Informatics, vol. 29, no. 1-2, pp. 257–265, 2011. View at Google Scholar
  9. J. Chen and Z. Li, “Common fixed-points for Banach operator pairs in best approximation,” Journal of Mathematical Analysis and Applications, vol. 336, no. 2, pp. 1466–1475, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. D. W. Boyd and J. S. W. Wong, “On nonlinear contractions,” Proceedings of the American Mathematical Society, vol. 20, pp. 458–464, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. S. Reich, “Some fixed point problems,” Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali, vol. 57, no. 3-4, pp. 194–198, 1974. View at Google Scholar
  12. M. A. Al-Thagafi, “Common fixed points and best approximation,” Journal of Approximation Theory, vol. 85, no. 3, pp. 318–323, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. M. A. Al-Thagafi and N. Shahzad, “Banach operator pairs, common fixed-points, invariant approximations, and *-nonexpansive multimaps,” Nonlinear Analysis A, vol. 69, no. 8, pp. 2733–2739, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. S. Chandok and T. D. Narang, “Some common fixed point theorems for Banach operator pairs with applications in best approximation,” Nonlinear Analysis A, vol. 73, no. 1, pp. 105–109, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. S. Chandok and T. D. Narang, “Common fixed points and invariant approximation for Gregus type contraction mappings,” Rendiconti del Circolo Matematico di Palermo, vol. 60, no. 1-2, pp. 203–214, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. Chandok and T. D. Narang, “Common fixed points and invariant approximation for banach operator Pairs with ćirić type nonexpansive mappings,” Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 6, pp. 871–883, 2011. View at Google Scholar · View at Scopus
  17. S. Chandok, J. Liang, and D. O'Regan, “Common fixed points and invariant approximations for noncommuting contraction mappings in strongly convex metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 14, 2013. View at Google Scholar
  18. L. Habiniak, “Fixed point theorems and invariant approximations,” Journal of Approximation Theory, vol. 56, no. 3, pp. 241–244, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. T. D. Narang and S. Chandok, “Fixed points and best approximation in metric spaces,” Indian Journal of Mathematics, vol. 51, no. 2, pp. 293–303, 2009. View at Google Scholar · View at Zentralblatt MATH
  20. T. D. Narang and S. Chandok, “Common fixed points and invariant approximation of R-subweakly commuting maps in convex metric spaces,” Ukrainian Mathematical Journal, vol. 62, no. 10, pp. 1585–1596, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. N. Shahzad, “Invariant approximations and R-subweakly commuting maps,” Journal of Mathematical Analysis and Applications, vol. 257, no. 1, pp. 39–45, 2001. View at Publisher · View at Google Scholar
  22. S. Singh, B. Watson, and P. Srivastava, Fixed Point Theory and Best Approximation: The KKM-map Principle, vol. 424, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.