Table of Contents
Journal of Operators
Volume 2016 (2016), Article ID 5250394, 9 pages
http://dx.doi.org/10.1155/2016/5250394
Research Article

Fractals of Generalized -Hutchinson Operator in -Metric Spaces

1Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, 72123 Västerås, Sweden
2Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad 22060, Pakistan

Received 29 April 2016; Accepted 22 June 2016

Academic Editor: Aref Jeribi

Copyright © 2016 Talat Nazir 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. J. E. Hutchinson, “Fractals and self-similarity,” Indiana University Mathematics Journal, vol. 30, no. 5, pp. 713–747, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. F. Barnsley, Fractals Everywhere, Academic Press, San Diego, Calif, USA, 2nd edition, 1993. View at MathSciNet
  3. S. Banach, “Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922. View at Google Scholar
  4. T. Abdeljawad, “Fixed points for generalized weakly contractive mappings in partial metric spaces,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 2923–2927, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. I. Arandjelović, Z. Kadelburg, and S. Radenović, “Boyd-Wong-type common fixed point results in cone metric spaces,” Applied Mathematics and Computation, vol. 217, no. 17, pp. 7167–7171, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. L.-G. Huang and X. Zhang, “Cone metric spaces and fixed point theorems of contractive mappings,” Journal of Mathematical Analysis and Applications, vol. 332, no. 2, pp. 1468–1476, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. D. Ilić, M. Abbas, and T. Nazir, “Iterative approximation of fixed points of Prešić operators on partial metric spaces,” Mathematische Nachrichten, vol. 288, no. 14-15, pp. 1634–1646, 2015. View at Publisher · View at Google Scholar
  8. A. Jeribi and B. Krichen, “Nonlinear functional analysis in Banach spaces and Banach algebras. Fixed point theory under weak topology for nonlinear operators and block operator matrices with applications,” in Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, Fla, USA, 2016. View at Google Scholar
  9. Z. Kadelburg, S. Radenović, and V. Rakočević, “Remarks on ‘Quasi-contraction on a cone metric space’,” Applied Mathematics Letters, vol. 22, no. 11, pp. 1674–1679, 2009. View at Publisher · View at Google Scholar
  10. E. Tarafdar, “An approach to fixed-point theorems on uniform spaces,” Transactions of the American Mathematical Society, vol. 191, pp. 209–225, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. W. Boyd and J. S. 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 MathSciNet
  12. M. Edelstein, “An extension of Banach's contraction principle,” Proceedings of the American Mathematical Society, vol. 12, pp. 7–10, 1961. View at Google Scholar · View at MathSciNet
  13. W. A. Kirk, “Fixed points of asymptotic contractions,” Journal of Mathematical Analysis and Applications, vol. 277, no. 2, pp. 645–650, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. A. Meir and E. Keeler, “A theorem on contraction mappings,” Journal of Mathematical Analysis and Applications, vol. 28, pp. 326–329, 1969. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. E. Rakotch, “A note on contractive mappings,” Proceedings of the American Mathematical Society, vol. 13, pp. 459–465, 1962. View at Publisher · View at Google Scholar · View at MathSciNet
  16. J. Nadler, “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, pp. 475–488, 1969. View at Publisher · View at Google Scholar · View at MathSciNet
  17. M. Abbas, M. R. Alfuraidan, and T. Nazir, “Common. Fixed points of multi-valued F-contractions on metric spaces with a directed graph,” Carpathian Journal of Mathematics, vol. 32, no. 1, pp. 1–12, 2016. View at Google Scholar
  18. 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
  19. M. Sgroi and C. Vetro, “Multi-valued F-contractions and the solution of certain functional and integral equations,” Filomat, vol. 27, no. 7, pp. 1259–1268, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. S. Czerwik, “Contraction mappings in b-metric spaces,” Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 1, pp. 5–11, 1993. View at Google Scholar · View at MathSciNet
  21. T. V. An, L. Q. Tuyen, and N. V. Dung, “Stone-type theorem on b-metric spaces and applications,” Topology and Its Applications, vol. 185-186, pp. 50–64, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. H. Aydi, M.-F. Bota, E. Karapınar, and S. Mitrović, “A fixed point theorem for set-valued quasi-contractions in b-metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 88, 8 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. M. Boriceanu, A. Petruşel, and I. A. Rus, “Fixed point theorems for some multivalued generalized contractions in b-metric spaces,” International Journal of Mathematics and Statistics, vol. 6, pp. 65–76, 2010. View at Google Scholar
  24. M. Boriceanu, M. Bota, and A. Petruşel, “Multivalued fractals in b-metric spaces,” Central European Journal of Mathematics, vol. 8, no. 2, pp. 367–377, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. L. Ćirić, M. Abbas, M. Rajović, and B. Ali, “Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 1712–1723, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. C. Chifu and G. Petruşel, “Fixed points for multivalued contractions in b-metric spaces with applications to fractals,” Taiwanese Journal of Mathematics, vol. 18, no. 5, pp. 1365–1375, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. S. Czerwik, K. Dlutek, and S. L. Singh, “Round-off stability of iteration procedures for operators in b-metric spaces,” Journal of Nature Physical Science, vol. 11, pp. 87–94, 1997. View at Google Scholar
  28. 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
  29. M. A. Kutbi, E. Karapınar, J. Ahmad, and A. Azam, “Some fixed point results for multi-valued mappings in b-metric spaces,” Journal of Inequalities and Applications, vol. 2014, article 126, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. J. R. Roshan, N. Hussain, S. Sedghi, and N. Shobkolaei, “Suzuki-type fixed point results in b-metric spaces,” Mathematical Sciences, vol. 9, no. 3, pp. 153–160, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  31. J. R. Roshan, V. Parvaneh, and I. Altun, “Some coincidence point results in ordered b-metric spaces and applications in a system of integral equations,” Applied Mathematics and Computation, vol. 226, pp. 725–737, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. T. Nazir, S. Silvestrov, and M. Abbas, “Fractals of generalized F-hutchinson operator,” Waves, Wavelets and Fractals—Advanced Analysis, vol. 2, pp. 29–40, 2016. View at Google Scholar
  33. D. Wardowski, “Fixed points of a new type of contractive mappings in complete metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 94, 6 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. D. Klim and D. Wardowski, “Fixed points of dynamic processes of set-valued F-contractions and application to functional equations,” Fixed Point Theory and Applications, vol. 2015, article 22, 9 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus