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Journal of Function Spaces
Volume 2017, Article ID 9389768, 11 pages
https://doi.org/10.1155/2017/9389768
Research Article

Common Fixed Points of Four Maps Satisfying -Contraction on -Metric Spaces

1Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan
2Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, China
3School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 10001, China
4Department of Mathematics, Gomal University D. I. Khan, Khyber Pakhtunkhwa 29050, Pakistan

Correspondence should be addressed to Ma Zhenhua; moc.361@1891_auhgnehzam

Received 16 October 2017; Accepted 7 December 2017; Published 28 December 2017

Academic Editor: Ahmad S. Al-Rawashdeh

Copyright © 2017 Muhammad Nazam 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. D. Wardowski, “Fixed points of a new type of contractive mappings in complete metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 94, 2012. View at Publisher · View at Google Scholar · View at Scopus
  2. O. Acar and I. Altun, “Multivalued F-contractive mappings with a graph and some fixed point results,” Publicationes Mathematicae, vol. 88, no. 3-4, pp. 305–317, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  3. M. U. Ali and T. Kamran, “Multivalued F-contractions and related fixed point theorems with an application,” Filomat, vol. 30, no. 14, pp. 3779–3793, 2016. View at Publisher · View at Google Scholar · View at Scopus
  4. G. Durmaz, G. Minak, and I. Altun, “Fixed points of ordered F-contractions,” Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 1, pp. 15–21, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  5. A. Hussain, M. Nazam, and M. Arshad, “Connection of ciric type F-contraction involving fixed point on closed ball,” Gazi University Journal of Science, vol. 30, no. 1, pp. 283–291, 2017. View at Google Scholar · View at Scopus
  6. A. Hussain, H. F. Ahmad, M. Arshad, and M. Nazam, “New type of multivalued F-contraction involving fixed points on closed ball,” Journal of Mathematics and Computer Science, vol. 17, no. 02, pp. 246–254, 2017. View at Publisher · View at Google Scholar
  7. H. Piri and P. Kumam, “Some fixed point theorems concerning F-contraction in complete metric spaces,” Fixed Point Theory and Applications, vol. 2014, no. 1, article 210, p. 11, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. N.-A. Secelean, “Iterated function systems consisting of F-contractions,” Fixed Point Theory and Applications, vol. 2013, article 277, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Cosentino and P. Vetro, “Fixed point results for F-contractive mappings of Hardy-Rogers-type,” Filomat, vol. 28, no. 4, pp. 715–722, 2014. View at Publisher · View at Google Scholar · View at Scopus
  10. G. Mınak, A. Helvacı, and I. Altun, “Ćirić type generalized F-contractions on complete metric spaces and fixed point results,” Filomat, vol. 28, no. 6, pp. 1143–1151, 2014. View at Publisher · View at Google Scholar · View at Scopus
  11. I. A. Bakhtin, “The contraction mapping principle in almost metric space,” Functional Analysis, vol. 30, pp. 26–37, 1989. View at Google Scholar · View at MathSciNet
  12. 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
  13. H. Huang, J. Vujaković, and S. Radenović, “A note on common fixed point theorems for isotone increasing mappings in ordered b-metric spaces,” Journal of Nonlinear Sciences and Applications, vol. 8, no. 5, pp. 808–815, 2015. View at Google Scholar · View at MathSciNet
  14. N. Hussain, D. Dorić, Z. Kadelburg, and S. Radenović, “Suzuki-type fixed point results in metric type spaces,” Fixed Point Theory and Applications, vol. 2012, article 126, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Radenović, M. Jovanović, and Z. Kadelburg, “Common fixed point results in metric-type spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 978121, p. 15, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. M. A. Khamsi and N. Hussain, “KKM mappings in metric type spaces,” Nonlinear Analysis, vol. 73, no. 9, pp. 3123–3129, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  17. V. Parvaneh, J. R. Roshan, and S. Radenović, “Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations,” Fixed Point Theory and Applications, vol. 2013, article 130, p. 19, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, and W. Shatanawi, “Common fixed points of almost generalized (ψ, φ) s-contractive mappings in ordered b-metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 159, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. W. Shatanawi, A. Pitea, and R. Lazović, “Contraction conditions using comparison functions on b-metric spaces,” Fixed Point Theory and Applications, vol. 2014, no. 1, article 135, 2014. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Aghajani, M. Abbas, and J. R. Roshan, “Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces,” Mathematica Slovaca, vol. 64, no. 4, pp. 941–960, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  21. A. Amini-Harandi, “Fixed point theory for quasi-contraction maps in b-metric spaces,” Fixed Point Theory, vol. 15, no. 2, pp. 351–358, 2014. View at Google Scholar · View at MathSciNet
  22. A. Latif, V. Parvaneh, P. Salimi, and A. E. Al-Mazrooei, “Various Suzuki type theorems in b-metric spaces,” Journal of Nonlinear Sciences and Applications, vol. 8, no. 4, pp. 363–377, 2015. View at Google Scholar · View at MathSciNet
  23. F. Zabihi and A. Razani, “Fixed point theorems for hybrid rational geraghty contractive mappings in ordered b-metric spaces,” Journal of Applied Mathematics, vol. 2014, Article ID 929821, 9 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  24. M. Cosentino, M. Jleli, B. Samet, and C. Vetro, “Solvability of integrodifferential problems via fixed point theory in b-metric spaces,” Fixed Point Theory and Applications, vol. 2015, no. 70, 2015. View at Publisher · View at Google Scholar · View at Scopus
  25. G. Jungck, “Compatible mappings and common fixed points,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 4, pp. 771–779, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  26. R. M. T. Bianchini, “Su un problema di S. Reich riguardante la teoria dei punti fissi,” The Bollettino dell'Unione Matematica Italiana, vol. 5, pp. 103–108, 1972. View at Google Scholar · View at MathSciNet
  27. V. M. Sehgal, “On fixed and periodic points for a class of mappings,” Journal Of The London Mathematical Society-Second Series, vol. 5, pp. 571–576, 1972. View at Google Scholar · View at MathSciNet
  28. L. B. Círíc, “A generalization of Banach's contraction principle,” Proceedings of the American Mathematical Society, vol. 45, pp. 267–273, 1974. View at Google Scholar · View at MathSciNet
  29. G. Jungck, “Common fixed points for commuting and compatible maps on compacta,” Proceedings of the American Mathematical Society, vol. 103, no. 3, pp. 977–983, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. S. Reich, “Some remarks concerning contraction mappings,” Canadian Mathematical Bulletin, vol. 14, pp. 121–124, 1971. View at Google Scholar · View at MathSciNet
  31. S. K. Chatterjea, “Fixed-point theorems,” Comptes rendus de l'Academie bulgare des Sciences, vol. 25, pp. 727–730, 1972. View at Google Scholar · View at MathSciNet