Skip to main content
Log in

On Common Fixed Points in the Context of Brianciari Metric Spaces

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we introduce the concept of generalized (\({\alpha,\psi}\))-contractions and generalized (\({\alpha,\psi}\))-Meir–Keeler-contractions in the setting of Brianciari metric spaces. We prove some common fixed point results for such contractions. An example is presented making effective the new concepts and results.

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. Ali M.U., Kamran T., Karapınar E.: On (\({\alpha,\psi,\eta}\))-contractive multivalued mappings. Fixed Point Theory Appl. 2014, 7 (2014)

    Article  MathSciNet  Google Scholar 

  2. Aydi, H.: \({\alpha}\)-implicit contractive pair of mappings on quasi b-metric spaces and application to integral equations. J. Nonlinear Convex Anal. (2015, accepted)

  3. Aydi H., Felhi A., Sahmim S.: Common fixed points in rectangular b-metric spaces using (E.A) property. J. Adv. Math. Studies 8(2), 159–169 (2015)

    MathSciNet  MATH  Google Scholar 

  4. Aydi, H., Felhi, A., sahmim, S.: On Common fixed points for \({(\alpha,F,\psi)}\)-contractions in partial metric spaces and an application. Analele Stiintifice ale Universitii Al.I. Cuza din Iasi (2015, in press)

  5. Aydi H., Jellali M., Karapinar E.: Common fixed points for generalized \({\alpha}\)-implicit contractions in partial metric spaces: consequences and application. RACSAM 109(2), 367–384 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Aydi H., Karapınar E.: Fixed point results for generalized \({\alpha}\)\({\psi}\)-contractions in metric-like spaces and applications. Electron. J. Differ. Equ. 2015(133), 1–15 (2015)

    MathSciNet  MATH  Google Scholar 

  7. Aydi H., Karapınar E., Lakzian H.: Fixed point results on the class of generalized metric spaces. Math. Sci. 6, 46 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Aydi H., Karapinar E., Samet B.: Fixed points for generalized \({(\alpha,\psi)}\)-contractions on generalized metric spaces. J. Inequal. Appl. 2014, 229 (2014)

    Article  MathSciNet  Google Scholar 

  9. Azam A., Arshad M.: Kannan fixed point theorems on generalized metric spaces. J. Nonlinear Sci. Appl. 1, 45–48 (2008)

    MathSciNet  MATH  Google Scholar 

  10. Azam A., Arshad M., Beg I.: Banach contraction principle on cone rectangular metric spaces. Appl. Anal. Discrete Math. 3, 236–241 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bilgili N., Karapınar E.: A note on “common fixed points for \({(\psi, \alpha, \beta)}\)-weakly contractive mappings in generalized metric spaces”. Fixed Point Theory Appl. 2013, 287 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  13. Branciari A.: A fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces. Publ. Math. Debrecen 57, 31–37 (2000)

    MathSciNet  MATH  Google Scholar 

  14. Jleli, M., Karapınar, E., Samet, B.: Fixed point results for \({\alpha-\psi_\lambda}\)contractions on gauge spaces and applications. Abstr. Appl. Anal., Article ID 730825 (2013)

  15. Di Bari C., Vetro P.: Common fixed points in generalized metric spaces. Appl. Math. Comput. 218(13), 7322–7325 (2012)

    MathSciNet  MATH  Google Scholar 

  16. Kirk W.A., Shahzad N.: Generalized metrics and Caristi’s theorem. Fixed Point Theory Appl. 2013, 129 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Latif A., Eshaghi Gordji M., Karapinar E., Sintunavarat W.: Fixed point results for generalized \({(\alpha,\psi)}\)-Meir–Keeler contractive mappings and applications. J. Inequal. Appl. 2014, 68 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. La Rosa V., Vetro P.: Common fixed points for \({\alpha}\)\({\psi}\)\({\varphi}\)-contractions in generalized metric spaces. Nonlinear Anal. Model. Control 19(1), 43–54 (2014)

    MathSciNet  MATH  Google Scholar 

  19. Samet B.: Discussion on: a fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces by A. Branciari. Publ. Math. Debrecen 76(4), 493–494 (2010)

    MathSciNet  MATH  Google Scholar 

  20. Samet B., Vetro C., Vetro P.: Fixed point theorems for \({\alpha}\)\({\psi}\)-contractive type mappings. Nonlinear Anal. 75, 2154–2165 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Erdal Karapınar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aydi, H., Karapınar, E. & Zhang, D. On Common Fixed Points in the Context of Brianciari Metric Spaces. Results Math 71, 73–92 (2017). https://doi.org/10.1007/s00025-015-0516-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-015-0516-5

Mathematics Subject Classification

Keywords

Navigation