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Journal of Applied Mathematics
Volume 2013, Article ID 310106, 12 pages
http://dx.doi.org/10.1155/2013/310106
Research Article

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

Institute of Research and Development of Processes, University of Basque Country, Campus of Leioa (Bizkaia)-Aptdo. Postal 644-Bilbao, 48080 Bilbao, Spain

Received 11 March 2013; Accepted 2 July 2013

Academic Editor: D. R. Sahu

Copyright © 2013 M. De la Sen. 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. Yao, M. A. Noor, Y.-C. Liou, and S. M. Kang, “Iterative algorithms for general multivalued variational inequalities,” Abstract and Applied Analysis, vol. 2012, Article ID 768272, 10 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. De la Sen, “Stable iteration procedures in metric spaces which generalize a Picard-type iteration,” Fixed Point Theory and Applications, vol. 2010, Article ID 953091, 15 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. Ratchagit and K. Ratchagit, “Asymptotic stability and stabilization of fixed points for iterative sequence,” International Journal of Research and Reviews in Computer Science, vol. 2, no. 4, pp. 987–989, 2011. View at Google Scholar
  4. D. Doric and R. Lazović, “Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications,” Fixed Point Theory and Applications, vol. 2011, article 40, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  5. L.J. Ciric, “Multi-valued nonlinear contraction mappings,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 7-8, pp. 2716–2723, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L.J. Ciric, “Fixed points for generalized multi-valued contractions,” Matematički Vesnik, vol. 9, no. 24, pp. 265–272, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. L. Singh, S. N. Mishra, and S. Jain, “Round-off stability for multi-valued maps,” Fixed Point Theory and Applications, vol. 2012, article 12, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. L. Singh, S. N. Mishra, R. Chugh, and R. Kamal, “General common fixed point theorems and applications,” Journal of Applied Mathematics, vol. 2012, Article ID 902312, 14 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. W. Laowang and B. Panyanak, “Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 20, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  10. H. Khandani, S. M. Vaezpour, and B. Sims, “Common fixed points of generalized multivalued contraction on complete metric spaces,” Journal of Computational Analysis and Applications, vol. 13, no. 6, pp. 1025–1038, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. Abbas, “Coincidence points of multivalued f-almost nonexpansive mappings,” Fixed Point Theory, vol. 13, no. 1, pp. 3–10, 2012. View at Google Scholar · View at MathSciNet
  12. Sh. Rezapour and P. Amiri, “Fixed point of multivalued operators on ordered generalized metric spaces,” Fixed Point Theory, vol. 13, no. 1, pp. 173–178, 2012. View at Google Scholar · View at MathSciNet
  13. A. Petruşel and G. Petruşel, “Multivalued Picard operators,” Journal of Nonlinear and Convex Analysis, vol. 13, no. 1, pp. 157–171, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. T. P. Petru, A. Petruşel, and J.-C. Yao, “Ulam-Hyers stability for operatorial equations and inclusions via nonself operators,” Taiwanese Journal of Mathematics, vol. 15, no. 5, pp. 2195–2212, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. K. Nashine and W. Shatanawi, “Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 1984–1993, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. K. Iséki, “On common fixed points of mappings,” Bulletin of the Australian Mathematical Society, vol. 10, pp. 365–370, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. K. Iseki, “Multi-valued contraction mappings in complete metric spaces,” Rendiconti del Seminario Matematico della Universita di Padova, vol. 53, pp. 15–19, 1975. View at Google Scholar · View at MathSciNet
  18. A. Rashid Butt, Fixed points of set valued maps [Ph.D. thesis], Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan, 2010.
  19. I. Beg and A. R. Butt, “Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces,” Mathematical Communications, vol. 15, no. 1, pp. 65–76, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M. Abbas, A. R. Khan, and T. Nazir, “Coupled common fixed point results in two generalized metric spaces,” Applied Mathematics and Computation, vol. 217, no. 13, pp. 6328–6336, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. Abbas, M. Ali Khan, and S. Radenović, “Common coupled fixed point theorems in cone metric spaces for w-compatible mappings,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 195–202, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  22. D. R. Sahu, S. M. Kang, and V. Sagar, “Approximation of common fixed points of a sequence of nearly nonexpansive mappings and solutions of variational inequality problems,” Journal of Applied Mathematics, vol. 2012, Article ID 902437, 12 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. S. Karpagam and S. Agrawal, “Best proximity point theorems for p-cyclic Meir-Keeler contractions,” Fixed Point Theory and Applications, vol. 2009, Article ID 197308, 9 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  24. M. De la Sen, “Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings,” Fixed Point Theory and Applications, vol. 2010, Article ID 572057, 23 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. Kikkawa and T. Suzuki, “Three fixed point theorems for generalized contractions with constants in complete metric spaces,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 69, no. 9, pp. 2942–2949, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. Y. Enjouji, M. Nakanishi, and T. Suzuki, “A generalization of Kannan's fixed point theorem,” Fixed Point Theory and Applications, vol. 2009, Article ID 192872, 10 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. M. S. Khan, “Common fixed point theorems for multivalued mappings,” Pacific Journal of Mathematics, vol. 95, no. 2, pp. 337–347, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. Y. J. Cho, J. K. Kim, and S. M. Kang, Fixed Point Theory and Applications, vol. 3, Nova Publishers, 2002.
  29. A. Ashyralyev and H. O. Fattorini, “On uniform difference schemes for second-order singular perturbation problems in Banach spaces,” SIAM Journal on Mathematical Analysis, vol. 23, no. 1, pp. 29–54, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. B. T. Kalimbetov, M. A. Temirbekov, and Z. O. Khabibullayev, “Asymptotic solutions of singular perturbed problems with an instable spectrum of the limiting operator,” Abstract and Applied Analysis, vol. 2012, Article ID 120192, 16 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. V. P. Maksimov and A. L. Chadov, “A class of controls for a functional-differential continuous-discrete system,” Russian Mathematics, vol. 56, no. 9, pp. 62–65, 2012. View at Google Scholar
  32. A. Ashyralyev and Y. A. Sharifov, “Existence and uniqueness of solutions for the system of nonlinear fractional differential equations with nonlocal and integral boundary conditions,” Abstract and Applied Analysis, vol. 2012, Article ID 594802, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. M. De la Sen, “About robust stability of Caputo linear fractional dynamic systems with time delays through fixed point theory,” Fixed Point Theory and Applications, vol. 2011, Article ID 867932, 19 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. D. Amanov and A. Ashyralyev, “Initial-boundary value problem for fractional partial differential equations of higher order,” Abstract and Applied Analysis, vol. 2012, Article ID 973102, 16 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. M. de la Sen, “Application of the nonperiodic sampling to the identifiability and model matching problems in dynamic systems,” International Journal of Systems Science, vol. 14, no. 4, pp. 367–383, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  36. M. de la Sen, “Stability of composite systems with an asymptotically hyperstable subsystem,” International Journal of Control, vol. 44, no. 6, pp. 1769–1775, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  37. H. Xiang and J. Cao, “Periodic oscillation of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients,” Journal of Applied Mathematics, vol. 2008, Article ID 453627, 18 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. M. De la Sen, R. P. Agarwal, A. Ibeas, and S. Alonso-Quesada, “On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls,” Advances in Difference Equations, vol. 2010, Article ID 281612, 42 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  39. Y. Zhang, “Asymptotic stability of impulsive reaction-diffusion cellular neural networks with time-varying delays,” Journal of Applied Mathematics, vol. 2010, Article ID 501891, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  40. L.-C. Ceng and J.-C. Yao, “A hybrid iterative scheme for mixed equilibrium problems and fixed point problems,” Journal of Computational and Applied Mathematics, vol. 214, no. 1, pp. 186–201, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  41. N. Hussain and M. A. Khamsi, “On asymptotic pointwise contractions in metric spaces,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 10, pp. 4423–4429, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  42. A. A. Eldred and P. Veeramani, “Existence and convergence of best proximity points,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1001–1006, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  43. I. A. Pyatyshev, “Operations on approximatively compact sets,” Mathematical Notes, vol. 82, no. 5, pp. 729–735, 2007. View at Publisher · View at Google Scholar · View at MathSciNet