Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 542302, 7 pages
http://dx.doi.org/10.1155/2013/542302
Research Article

Endpoints of Multivalued Contraction Operators

Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sector-62, Noida 201307, India

Received 19 July 2013; Accepted 30 September 2013

Academic Editors: R. D. Chen, F. Colombini, and K. Lurie

Copyright © 2013 Bhagwati Prasad and Ritu Sahni. 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. S. B. Nadler, Jr., “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, pp. 475–488, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. N. A. Assad and W. A. Kirk, “Fixed point theorems for set-valued mappings of contractive type,” Pacific Journal of Mathematics, vol. 43, pp. 553–562, 1972. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J.-P. Aubin and J. Siegel, “Fixed points and stationary points of dissipative multivalued maps,” Proceedings of the American Mathematical Society, vol. 78, no. 3, pp. 391–398, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Pure and Applied Mathematics (New York), John Wiley & Sons, New York, NY, USA, 1984. View at MathSciNet
  5. L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, vol. 495 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999. View at MathSciNet
  6. A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2003. View at MathSciNet
  7. R. Węgrzyk, “Fixed-point theorems for multivalued functions and their applications to functional equations,” Dissertationes Mathematicae, vol. 201, pp. 1–28, 1982. View at Google Scholar · View at MathSciNet
  8. E. Zeidler, Nonlinear Functional Analysis and Its Applications I: Fixed Point Theorems, Springer, New York, NY, USA, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  9. I. A. Rus, “Strict fixed point theory,” Fixed Point Theory, vol. 4, no. 2, pp. 177–183, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. Amini-Harandi, “Endpoints of set-valued contractions in metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 1, pp. 132–134, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. N. Hussain, A. Amini-Harandi, and Y. J. Cho, “Approximate endpoints for set-valued contractions in metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 614867, 13 pages, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Moradi and F. Khojasteh, “Endpoints of multi-valued generalized weak contraction mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 6, pp. 2170–2174, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K. Włodarczyk, D. Klim, and R. Plebaniak, “Existence and uniqueness of endpoints of closed set-valued asymptotic contractions in metric spaces,” Journal of Mathematical Analysis and Applications, vol. 328, no. 1, pp. 46–57, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. K. Włodarczyk and R. Plebaniak, “Endpoint theory for set-valued nonlinear asymptotic contractions with respect to generalized pseudodistances in uniform spaces,” Journal of Mathematical Analysis and Applications, vol. 339, no. 1, pp. 344–358, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. K. Włodarczyk, R. Plebaniak, and C. Obczyński, “Endpoints of set-valued dynamical systems of asymptotic contractions of Meir-Keeler type and strict contractions in uniform spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 6, pp. 1668–1679, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. Czerwik, “Nonlinear set-valued contraction mappings in b-metric spaces,” Atti del Seminario Matematico e Fisico dell'Università di Modena, vol. 46, no. 2, pp. 263–276, 1998. View at Google Scholar · View at MathSciNet
  17. S. L. Singh and B. Prasad, “Some coincidence theorems and stability of iterative procedures,” Computers & Mathematics with Applications, vol. 55, no. 11, pp. 2512–2520, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet