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The Scientific World Journal
Volume 2014, Article ID 784207, 14 pages
http://dx.doi.org/10.1155/2014/784207
Research Article

Fixed Point Theorems for Generalized α-β-Weakly Contraction Mappings in Metric Spaces and Applications

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhon Pathom 73140, Thailand
3Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12121, Thailand

Received 17 March 2014; Accepted 18 April 2014; Published 7 May 2014

Academic Editor: S. A. Mohiuddine

Copyright © 2014 Abdul Latif 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.

Citations to this Article [13 citations]

The following is the list of published articles that have cited the current article.

  • Marwan Amin Kutbi, and Wutiphol Sintunavarat, “Fixed point theorems for generalized w(alpha)-contraction multivalued mappings in alpha-complete metric spaces,” Fixed Point Theory And Applications, 2014. View at Publisher · View at Google Scholar
  • Poom Kumam, and Wutiphol Sintunavarat, “The existence of fixed point theorems for partial q-set-valued quasi-contractions in b-metric spaces and related results,” Fixed Point Theory And Applications, 2014. View at Publisher · View at Google Scholar
  • Supak Phiangsungnoen, and Poom Kumam, “Generalized Ulam-Hyers stability and well-posedness for fixed point equation via alpha-admissibility,” Journal Of Inequalities And Applications, 2014. View at Publisher · View at Google Scholar
  • Mehdi Asadi, Erdal Karapinar, and Anil Kumar, “alpha-psi-Geraghty contractions on generalized metric spaces,” Journal Of Inequalities And Applications, 2014. View at Publisher · View at Google Scholar
  • Farzaneh Zabihi, and Abdolrahman Razani, “PPF dependent fixed point theorems for αc-admissible rational type contractive mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2014, no. 1, pp. 197, 2014. View at Publisher · View at Google Scholar
  • Oratai Yamaod, Wutiphol Sintunavarat, and Yeol Je Cho, “Common fixed point theorems for generalized cyclic contraction pairs in b-metric spaces with applications,” Fixed Point Theory and Applications, vol. 2015, no. 1, 2015. View at Publisher · View at Google Scholar
  • Wutiphol Sintunavarat, “Fixed point results in b-metric spaces approach to the existence of a solution for nonlinear integral equations,” Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2015. View at Publisher · View at Google Scholar
  • Oratai Yamaod, Wutiphol Sintunavarat, and Yeol Je Cho, “Existence of a common solution for a system of nonlinear integral equations via fixed point methods in b-metric spaces,” Open Mathematics, vol. 14, pp. 128–145, 2016. View at Publisher · View at Google Scholar
  • Wutiphol Sintunavarat, and Aphinat Ninsri, “Approximation fixed theorems for α-partial weakly Zamfirescu mappings with application to homotopy invariance,” Filomat, vol. 30, no. 7, pp. 1941–1956, 2016. View at Publisher · View at Google Scholar
  • Wutiphol Sintunavarat, and Chirasak Mongkolkeha, “Optimal approximate solution for (α,ß)ψ-contraction mappings in metric spaces with applications,” Applied Mathematics and Information Sciences, vol. 10, no. 2, pp. 507–518, 2016. View at Publisher · View at Google Scholar
  • Vasile Berinde, and Mădălina Păcurar, “Iterative Approximation of Fixed Points of Single-valued Almost Contractions,” Fixed Point Theory and Graph Theory, pp. 29–97, 2016. View at Publisher · View at Google Scholar
  • Oratai Yamaod, and Wutiphol Sintunavarat, “The existence theorem for a solution of a system of integral equations along with cyclical common fixed point technique,” Journal of Fixed Point Theory and Applications, vol. 19, no. 2, pp. 1535–1549, 2017. View at Publisher · View at Google Scholar
  • Chirasak Mongkolkeha, and Poom Kumam, “Some existence of coincidence point and approximate solution method for generalized weak contraction in b-generalized pseudodistance fiunctions,” Filomat, vol. 31, no. 19, pp. 6185–6203, 2017. View at Publisher · View at Google Scholar