Advertisement

The Journal of Analysis

, Volume 27, Issue 4, pp 1109–1121 | Cite as

Common fixed point theorems for \(F^*\)-contraction mappings with an application

  • S. MuralisankarEmail author
  • A. Santhi
Original Research Paper
  • 50 Downloads

Abstract

The aim of this paper is to define \(F^*\)-contraction for pair of self mappings and prove some common fixed point theorems in the context of compatible mappings. Finally, we give some examples and an application to validate our main results.

Keywords

Fixed point Compatible mappings Complete metric space \(F^*\)-contraction 

Mathematics Subject Classification

47H10 54H25 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Ahmad, J., Al-Rawashdeh, A., and A. Azam. 2015. New fixed point theorems for generalized F-contraction in complete metric spaces. Fixed Point Theory Applications 80: 1–18.Google Scholar
  2. 2.
    Berinde, V. 2009. A common fixed point theorem for compatible quasi contractive self mappings in metric spaces. Applied Mathematics and Computation 213: 348–354.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ciric, Lj, A. Razani, S. Radenovic, and J.S. Ume. 2008. Common fixed point theorems for families of weakly compatible maps. Computers and Mathematics with Applications 55: 2533–2543.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dung, N.V., and V.L. Hang. 2015. A fixed point theorem for generalized F-contraction on complete metric spaces. Vietnam Journal of Mathematics 43: 743–753.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hussain, N., J. Ahmad, and A. Azam. 2015. On Suzuki-Wardowski type fixed point theorems. Journal of Nonlinear Science and Applications 8: 1095–1111.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jungck, G. 1976. Commuting mappings and fixed points. The American Mathematical Monthly 83: 261–263.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Jungck, G. 1986. Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences 9: 771–779.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Jungck, G. 1988. Compatible mappings and common fixed points (2). International Journal of Mathematics and Mathematical Sciences 11: 285–288.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pant, R.P. 1999. A common fixed point theorem under a new condition. Indian Journal of Pure and Applied Mathematics 32 (2): 147–152.MathSciNetzbMATHGoogle Scholar
  10. 10.
    Piri, H., and P. Kumam. 2014. Some fixed point theorems concerning F-contraction in complete metric spaces. Fixed Point Theory Applications 210: 1–11.MathSciNetzbMATHGoogle Scholar
  11. 11.
    Piri, H., and P. Kumam. 2016. Wardowski type fixed point theorems in complete metric spaces. Fixed Point Theory Applications 45: 1–12.MathSciNetzbMATHGoogle Scholar
  12. 12.
    Sgroi, M., and C. Vetro. 2013. Multivalued F-contraction and the solution of certain functional and integral equations. Filomat 27 (7): 1259–1268.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Singh, S.L., and S.P. Singh. 1980. Fixed point theorem. Indian Journal of Pure and Applied Mathematics. 11: 1584–1586.MathSciNetzbMATHGoogle Scholar
  14. 14.
    Wardowski, D. 2012. Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Applications 94: 1–6.MathSciNetzbMATHGoogle Scholar
  15. 15.
    Wardowski, D., and N.V. Dung. 2014. Fixed points of F-weak contraction on complete metric spaces. Demonstratio Mathematica XLVII:146–155.Google Scholar

Copyright information

© Forum D'Analystes, Chennai 2019

Authors and Affiliations

  1. 1.School of MathematicsMadurai Kamaraj UniversityMaduraiIndia

Personalised recommendations