Skip to main content
Log in

Coincidence point theorems on quasi-metric spaces via simulation functions and applications to G-metric spaces

  • Published:
Journal of Fixed Point Theory and Applications Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper, we present some coincidence point results in the framework of quasi-metric spaces using contractive conditions involving simulation functions. As consequences, we are able to particularize these results to a variety of situations including G-metric spaces. The results presented in this paper generalize and extend several comparable results in the existing literature. In addition, some examples are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aage, C.T., Salunke, J.N.: Fixed points for weak contractions in \(G\)-metric spaces. Appl. Math. E-Notes 12, 23–28 (2012)

    MathSciNet  MATH  Google Scholar 

  2. Agarwal, R.P., Karapınar, E.: Remarks on some coupled fixed point theorems in \(G\)-metric spaces. Fixed Point Theory Appl. 2013, 2 (2013). (Article ID 2013)

    Article  MathSciNet  Google Scholar 

  3. Agarwal, R.P., Karapınar, E., O’Regan, D., Roldán López de Hierro, A.F.: Fixed Point Theory in Metric Type Spaces. Springer, Switzerland (2015)

    Book  Google Scholar 

  4. Agarwal, R.P., Karapınar, E., Roldán, A.: Fixed point theorems in quasi-metric spaces and applications to multidimensional fixed points on \(G^{\ast }\)-metric spaces. J. Nonlinear Convex Anal. 16(9), 1787–1816 (2015)

    MathSciNet  MATH  Google Scholar 

  5. Aguirre Salazar, L., Reich, S.: A remark on weakly contractive mappings. J. Nonlinear Convex Anal. 16, 767–773 (2015)

    MathSciNet  MATH  Google Scholar 

  6. Alsulami, H.H., Karapınar, E., Khojasteh, F., Roldán López de Hierro, A.F.: A proposal to the study of contractions in quasi-metric spaces. Discret. Dyn. Nat. Soc. 2014, 10 (2014). (Article ID 269286)

    Article  MathSciNet  Google Scholar 

  7. Argoubi, H., Samet, B., Vetro, C.: Nonlinear contractions involving simulation functions in a metric space with a partial order. J. Nonlinear Sci. Appl. 8(6), 1082–1094 (2015)

    Article  MathSciNet  Google Scholar 

  8. Aydi, H., Felhi, A., Sahmim, S.: Related fixed point results for cyclic contractions on \(G\)-metric spaces and application. Filomat 31(3), 853–869 (2017)

    Article  MathSciNet  Google Scholar 

  9. Aydi, H., Mustafa, Z., Karapınar, E.: Generalized Meir–Keeler type contractions on \(G\)-metric spaces. Appl. Math. Comput. 219(21), 10441–10447 (2013)

    MathSciNet  MATH  Google Scholar 

  10. Aydi, H., Shatanawi, W., Vetro, C.: On generalized weakly \(G\)-contraction mapping in \(G\)-metric spaces. Comput. Math. Appl. 62(11), 4222–4229 (2011)

    Article  Google Scholar 

  11. Banach, S.: Sur les opérations dans les ensembles abstraits et leur application auxéquations intégrales. Fundam. Math. 3, 133–181 (1922)

    Article  Google Scholar 

  12. Bilgili, N., Karapınar, E., Samet, B.: Generalized \(\alpha \)-\(\psi \)-contractive mappings in quasi-metric spaces and related fixed-point theorems. J. Ineq. Appl. 2014, 36 (2014). (Article ID 2014)

    Article  MathSciNet  Google Scholar 

  13. Boyd, D.W., Wong, J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20(2), 458–464 (1969)

    Article  MathSciNet  Google Scholar 

  14. Browder, F.E., Petrysyn, W.V.: The solution by iteration of nonlinear functional equation in Banach spaces. Bull. Am. Math. Soc. 72, 571–576 (1966)

    Article  MathSciNet  Google Scholar 

  15. Jleli, M., Samet, B.: Remarks on \(G\)-metric spaces and fixed point theorems. Fixed Point Theory Appl. 2012, 210 (2012). (Article ID 2012)

    Article  MathSciNet  Google Scholar 

  16. Khan, M.S., Swaleh, M., Sessa, S.: Fixed point theorems by altering distances between the points. Bull. Aust. Math. Soc. 30(1), 1–9 (1984)

    Article  MathSciNet  Google Scholar 

  17. Khojasteh, F., Rakočević, V.: Some new common fixed point results for generalized contractive multi-valued non-self-mappings. Appl. Math. Lett. 25, 287–293 (2012)

    Article  MathSciNet  Google Scholar 

  18. Khojasteh, F., Shukla, S., Radenović, S.: A new approach to the study of fixed point theorems via simulation functions. Filomat 29(6), 1189–1194 (2015)

    Article  MathSciNet  Google Scholar 

  19. Mizoguchi, N., Takahashi, W.: Fixed point theorems for multivalued mappings on complete metric spaces. J. Math. Anal. Appl. 141, 177–188 (1989)

    Article  MathSciNet  Google Scholar 

  20. Mustafa, Z.: A New Structure for Generalized Metric Spaces with Applications to Fixed Point Theory. Ph.D. Thesis, The University of Newcastle, Australia (2005)

  21. Mustafa, Z., Sims, B.: A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7, 289–297 (2006)

    MathSciNet  MATH  Google Scholar 

  22. Mustafa, Z., Sims, B.: Fixed point theorems for contractive mappings in complete \(G\)-metric spaces. Fixed Point Theory Appl. 2009, 10 (2009). (Article ID 917175)

    Article  MathSciNet  Google Scholar 

  23. Rhoades, B.E.: A comparison of various definitions of contractive mappings. Trans. Am. Math. Soc. 224, 257–290 (1977)

    Article  MathSciNet  Google Scholar 

  24. Rhoades, B.E.: Some theorems on weakly contractive maps. Nonlinear Anal. TMA 47, 2683–2693 (2001)

    Article  MathSciNet  Google Scholar 

  25. Roldán López de Hierro, A.F., Karapınar, E., Roldán López de Hierro, C., Martínez-Moreno, J.: Coincidence point theorems on metric spaces via simulation functions. J. Comput. Appl. Math. 275, 345–355 (2015)

    Article  MathSciNet  Google Scholar 

  26. Roldán López de Hierro, A.F., Samet, B.: \(\varphi \)-Admissibility results via extended simulation functions. J. Fix. Point Theory A. 19(3), 1997–2015 (2017)

    Article  MathSciNet  Google Scholar 

  27. Samet, B., Vetro, C., Vetro, F.: Remarks on \(G\)-metric spaces. Intern. J. Anal. 2013, 6 (2013). (Article ID 917158)

    MathSciNet  MATH  Google Scholar 

  28. Samet, B., Karapınar, E., Roldán López de Hierro, A.F.: Matkowski theorems in the context of quasi-metric spaces and consequences on \(G\)-metric spaces. An. Sti. U. Ovid. Co-Mat. 24(1), 309–333 (2016)

    MathSciNet  MATH  Google Scholar 

  29. Shatanawi, W.: Fixed point theory for contractive mappings satisfying \(\phi \)-maps in \(G\)-metric spaces. Fixed Point Theory Appl. 2010, 9 (2010). (Article ID 181650)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

A.F. Roldán López de Hierro has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE and by Project TIN2017-89517-P of the Ministerio de Economía, Industria y Competitividad.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

Corresponding author

Correspondence to A. F. Roldán López de Hierro.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Roldán López de Hierro, A.F., Karapınar, E. & O’Regan, D. Coincidence point theorems on quasi-metric spaces via simulation functions and applications to G-metric spaces. J. Fixed Point Theory Appl. 20, 112 (2018). https://doi.org/10.1007/s11784-018-0582-x

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s11784-018-0582-x

Mathematics Subject Classification

Keywords

Navigation