Some fixed point theorems for \(\theta\)-\(\phi\) \({C}\)-contractions

Volume 10, Issue 11, pp 5723--5733 http://dx.doi.org/10.22436/jnsa.010.11.10

Publication Date: November 15, 2017 Submission Date: May 18, 2017

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2513 Downloads
• 4087 Views

Authors

Dingwei Zheng - College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China. Xinhe Liu - College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China. Gengrong Zhang - College of Mathematics and Computationl Science, Hunan First Normal University, Changsha, Hunan, 410205, P. R. China.

Abstract

In this paper, we introduce the notion of \(\theta\)-\(\phi\) \({C}\)-contraction and establish some fixed point and coupled fixed point theorems for these mappings in the setting of complete metric spaces and ordered metric spaces. The results presented in the paper improve and extend some well-known results. Also, we give an example to illustrate them.

Share and Cite

Keywords

• Fixed point
• coupled fixed point
• complete metric space
• \(\theta\)-\(\phi\) \({C}\)-contraction

MSC

•  47H10
•  54H25

References

• [1] F. Bojor , Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895–3901.
  • View Article
  • MathSciNet
  • Google Scholar


• [2] D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458–464.
  • Google Scholar


• [3] F. E. Browder , On the convergence of successive approximations for nonlinear functional equations, Indag. Math., 71 (1968), 27–35.
  • MathSciNet
  • Google Scholar


• [4] S. K. Chatterjea, Fixed-point theorems , C. R. Acad. Bulgare Sci., 25 (1972), 727–730.


• [5] B. S. Choudhury , Unique fixed point theorem for weakly C-contractive mappings, Kathmandu Univ. J. Sci. Eng. Technol., 5 (2009), 6–13.
  • View Article
  • Google Scholar


• [6] B. S. Choudhury, A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., 73 (2010), 2524–2531.
  • View Article
  • MathSciNet
  • Google Scholar


• [7] J. Dugundji, A. Granas, Weakly contractive maps and elementary domain invariance theorem, Bull. Soc. Math. Gréce (N.S.), 19 (1978), 141–151.
  • MathSciNet
  • Google Scholar
  • MATH


• [8] Z. M. Fadail, A. G. B. Ahmad, G. S. Rad, V. Ozturk, S. Radenović , Some remarks on coupled, tripled and n-tupled coincidence and fixed points theorems in ordered abstract metric spaces, Far East J. Math. Sci., 97 (2015), 809–839.
  • View Article
  • Google Scholar
  • MATH


• [9] T. Gnana Bhaskar, V. Lakshmikantham , Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379–1393.
  • View Article
  • Google Scholar


• [10] J. Harjani, B. López, K. Sadarangani , Fixed point theorems for weakly C-contractive mappings in ordered metric spaces, Comput. Math. Appl., 61 (2011), 790–796.
  • View Article
  • MathSciNet
  • Google Scholar


• [11] J. R. Jachymski , Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., 125 (1997), 2327–2335.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 8 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [13] R. Kannan, Some results on fixed points, II, Amer. Math. Monthly, 76 (1969), 405–408.
  • View Article
  • Google Scholar


• [14] J. Matkowski, Integrable solutions of functional equations, Dissertationes Math. (Rozprawy Mat.), 127 (1975), 68 pages.
  • Google Scholar


• [15] H. Piri, P. Kumam , Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] S. Radenović , Remarks on some coupled fixed point results in partial metric spaces, Nonlinear Funct. Anal. Appl., 18 (2013), 39–50.
  • Google Scholar
  • MATH


• [17] S. Radenović, A note on tripled coincidence and tripled common fixed point theorems in partially ordered metric spaces, Appl. Math. Comput., 236 (2014), 367–372.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] S. Radenović, Bhaskar-Lakshmikantham type results for monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 5 (2014), 96–103.
  • Google Scholar
  • MATH


• [19] S. Radenović, Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Kragujevac J. Math., 38 (2014), 249–257.
  • View Article
  • MathSciNet
  • Google Scholar


• [20] S. Radenović, Remarks on some coupled coincidence point results in partially ordered metric spaces, Arab J. Math. Sci., 20 (2014), 29–39.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] B. Samet , Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 72 (2010), 4508–4517.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [22] 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


• [23] W. Shatanawi, Fixed point theorems for nonlinear weakly C-contractive mappings in metric spaces, Math. Comput. Modelling, 54 (2011), 2816–2826.
  • View Article
  • MathSciNet
  • Google Scholar


• [24] D. Wardowski , Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 6 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [25] D.-W. Zheng, Z.-Y. Cai, P. Wang , New fixed point theorems for \(\theta-\phi\) contraction in complete metric spaces, J. Nonlinear Sci. Appl., 10 (2017), 2662–2670.
  • View Article
  • MathSciNet
  • Google Scholar