Common fixed points for pairs of triangular \(\alpha\)-admissible mappings

Volume 10, Issue 12, pp 6192--6204 http://dx.doi.org/10.22436/jnsa.010.12.06

Publication Date: December 06, 2017 Submission Date: May 06, 2017

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Authors

Haitham Qawagneh - School of mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia. Mohd Salmi MD Noorani - School of mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia. Wasfi Shatanawi - Department of Mathematics and General Courses, Prince Sultan University, Riyadh, Saudi Arabia. - Department of Mathematics, Hashemite University, Zarqa, Jordan. Habes Alsamir - Department of Mathematics and General Courses, Aljouf University, Aljouf, Saudi Arabia.

Abstract

In this paper, we introduce the notation of \((\alpha-\eta)-(\psi-\varphi)\)-contraction mappings defined on a set \(X\). We prove the existence of common fixed point results for the pair of self-mappings involving C-class functions in the setting of metric space. Our results generalize and extend several works existing in literature. We provide an example and some applications in order to support our results.

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Keywords

• C-class functions
• \(\alpha\)-admissible mapping
• common fixed point
• metric spaces

MSC

•  47H09
•  47H10

References

• [1] P. Chuadchawna, A. Kaewcharoen and S. Plubtieng, Fixed point theorems for generalized \(\alpha-\eta-\psi\)-Geraghty contraction type mappings in \(\alpha-\eta-\psi\)-complete metric spaces , J. Nonlinear Sci. Appl., 9 (2016), 471–485.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] S. Alizadeh, F. Moradlou, P. Salimi , Some fixed point results for \((\alpha,\beta) - (\psi,\phi)\)-contractive mappings, Filomat, 28 (2014), 635–647.
  • Google Scholar


• [3] H. Alsamir, M. S. Noorani, W. Shatanawi, F. Shaddad, GeGeneralized Berinde-type (\(\eta,\xi,\vartheta,\theta\)) contractive mappings in B-metric spaces with an application, J. Math. Anal., 6 (2016), 1–12.
  • MathSciNet
  • Google Scholar
  • MATH


• [4] A. H. Ansari , Note on \(\varphi-\psi\)-contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, Tehran, (2014), 377–380.
  • Google Scholar


• [5] A. H. Ansari, J. Kaewcharoen, C-class functions and fixed point theorems for generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings in --complete metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 4177–4190.
  • View Article
  • Google Scholar
  • MATH


• [6] A. H. Ansari, W. Shatanawi, A. kurdi, G. Maniu , Best proximity points in complete metric spaces with (P)-property via C-class functions, J. Math. Anal., 7 (2016), 54–67.
  • MathSciNet
  • Google Scholar
  • MATH


• [7] P. Das, L. K. Dey , A fixed point theorem in a generalized metric space, Soochow J. Math., 33 (2007), 33–39.
  • Google Scholar


• [8] N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in \(\alpha\)-complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [9] N. Hussain, P. Salimi, A. Latif , Fixed point results for single and set-valued \(\alpha-\eta-\psi-\)contractive mappings, Fixed Point Theory Appl., 2013 (2013), 23 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] E. Karapınar , \(\alpha-\psi\)-Geraghty contraction type mappings and some related fixed point results, Filomat, 28 (2014), 37–48.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] E. Karapınar, P. Kumam, P. Salimi, On \(\alpha-\psi\)-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 12 pages.
  • Google Scholar


• [12] M. S. Khan, A fixed point theorem for metric spaces, Rend. Ist. Mat. Univ. Trieste, 8 (1976), 69–72.
  • Google Scholar


• [13] M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1–9.
  • View Article
  • Google Scholar


• [14] D. K. Patel, T. Abdeljawad, D. Gopal , Common fixed points of generalized Meir-Keeler \(\alpha\)-contractions , Fixed Point Theory Appl., 2013 (2013), 16 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [15] J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei,W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi)_s\)- contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 23 pages.
  • View Article
  • MathSciNet
  • MATH


• [16] P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 19 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [17] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings , Nonlinear Anal., 75 (2012), 2154–2165.
  • View Article
  • Google Scholar


• [18] W. Shatanawi, M. S. Noorani, H. Alsamir, A. Bataihah, Fixed and common fixed point theorems in partially ordered quasi-metric spaces, J. Math. Computer. Sci., 16 (2016), 516–528.
  • Google Scholar


• [19] W. Shatanawi, M. Postolache , Common fixed point results for mappings under nonlinear contraction of cyclic form in ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), 13 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH