Skip to main content
SpringerLink
Log in

On Weakly Commuting Set-Valued Mappings on a Domain of Sets Endowed with Directed Graph

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

The aim of this paper is to present coincidence and common fixed point results of set-valued mappings satisfying certain generalized graphic F-contractive conditions on a family of sets endowed with a graph. It is worth mentioning that these results are obtained without appealing to any form of continuity of mappings involved herein. Some examples are presented to support the results proved in this paper. Our results unify, generalize and extend various comparable results in the existing literature.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abbas, M., Alfuraidan, M.R., Khan, A.R., Nazir T.: Fixed point results for set-contractions on metric spaces with a directed graph. Fixed Point Theory Appl. 14, 09 (2015)

  2. Abbas M., Alfuraidan M.R., Nazir T.: Common fixed points of multivalued F-contractions on metric spaces with a directed graph. Carpathian J. Math. 32(1), 1–12 (2016)

    MathSciNet  Google Scholar 

  3. Abbas, M., Nazir, T.: Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph. Fixed Point Theory Appl. 20, 8 (2013)

  4. Abbas M., Jungck G.: Common fixed point results for noncommuting mappings without continuity in cone metric spaces. J. Math. Anal. Appl. 341, 416–420 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Aleomraninejad S.M.A., Rezapoura Sh., Shahzad N.: Some fixed point results on a metric space with a graph. Topol. Appl. 159, 659–663 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Alfuraidan, M.R., Khamsi, M.A.: Caristi fixed point theorem in metric spaces with a graph. Abstract Appl. Anal. 303484 (2014). doi:10.1155/2014/303484

  7. Amini-Harandi A., Emami H.: A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations. Nonlinear Anal. 72, 2238–2242 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Assad N.A., Kirk W.A.: Fixed point theorems for set-valued mappings of contractive type. Pacific. J. Math. 43, 533–562 (1972)

    Article  Google Scholar 

  9. Beg I., Butt A.R.: Fixed point theorems for set valued mappings in partially ordered metric spaces. Inter. J. Math. Sci. 7(2), 66–68 (2013)

    Google Scholar 

  10. Beg I., Butt A.R.: Fixed point of set-valued graph contractive mappings. J. Ineq. Appl. 52, 7 (2013)

    MATH  Google Scholar 

  11. Bojor F.: Fixed point of \({\varphi}\)-contraction in metric spaces endowed with a graph. Annals Uni. Craiova Math. Comp. Sci. Ser. 37(4), 85–92 (2010)

    MathSciNet  MATH  Google Scholar 

  12. Bojor F.: Fixed point theorems for Reich type contractions on metric spaces with a graph. Nonlinear Anal. 75, 3895–3901 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Bojor, F.: On Jachymski’s theorem. Annals Uni. Craiova Math. Comp. Sci. Ser. 40(1), 75, 23-28 (2012)

  14. Chifu, C.I., Petrusel, G.R.: Generalized contractions in metric spaces endowed with a graph. Fixed Point Theory Appl. 161 (2012). doi:10.1186/1687-1812-2012-161

  15. Edelstein M.: An extension of Banach’s contraction principle. Proc. Amer. Math. Soc. 12, 7–10 (1961)

    MathSciNet  MATH  Google Scholar 

  16. Gwozdz-Lukawska G., Jachymski J.: IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem. J. Math. Anal. Appl. 356, 453–463 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Harjani J., Sadarangani K.: Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Anal. 71, 3403–3410 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jachymski J., Jozwik I.: Nonlinear contractive conditions: a comparison and related problems. Banach Center Publ. 77, 123–146 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Jachymski J.: The contraction principle for mappings on a metric space with a graph. Proc. Amer. Math. Soc. 136, 1359–1373 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Jungck G.: Common fixed points for noncontinuous nonself maps on nonmetric spaces. Far East J. Math. Sci. 4, 199–215 (1996)

    MathSciNet  MATH  Google Scholar 

  21. Khan, A.R., Abbas, M., Nazir, T., Ionescu, C.: Fixed points of multivalued mappings in partial metric spaces. Abstract Appl. Anal. Volume 2014, 9. Article ID 230708 (2014)

  22. Klim, D., Wardowski, D.: Fixed points of dynamic processes of set-valued F-contractions and application to functional equations. Fixed Point Theory Appl. 22, 9 (2015)

  23. Nadler S.B.: Multivalued contraction mappings. Pacific J. Math. 30, 475–488 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  24. Nieto J.J., López R.R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order. 22, 223–239 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Nicolae A., O’Regan D., Petrusel A.: Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph. J. Georgian Math. Soc. 18, 307–327 (2011)

    MathSciNet  MATH  Google Scholar 

  26. Ran A.C.M., Reurings M.C.B.: A fixed point theorem in partially ordered sets and some application to matrix equations. Proc. Amer. Math. Soc. 132, 1435–1443 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  27. Sgroi M., Vetro C.: Multi-valued F-contractions and the solution of certain functional and integral equations. Filomat. 27(7), 1259–1268 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wardowski, D.: Fixed points of new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012)

Download references

Author information

Authors and Affiliations

  1. Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mujahid Abbas

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mujahid Abbas

  3. Division of Applied Mathematics, School of Education Culture and Communication, Mälardalen University, 72123, Västerås, Sweden

    Talat Nazir

  4. Department of Mathematics, COMSATS Institute of Information Technology, 22060, Abbottabad, Pakistan

    Talat Nazir

  5. Faculty of Science, University of Kragujevac, Radoja Domanovića 12, 34000, Kragujevac, Serbia

    Branislav Popović

  6. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia

    Stojan Radenović

  7. Department of Mathematics, State University of Novi Pazar, Novi Pazar, Serbia

    Stojan Radenović

Authors
  1. Mujahid Abbas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Talat Nazir
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Branislav Popović
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stojan Radenović
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Branislav Popović.

Additional information

The Branislav Popović were supported in part by the Serbian Ministry of Science and Technological Developments (Project: Methods of Numerical and Nonlinear Analysis with Applications, grant number #174002).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abbas, M., Nazir, T., Popović, B. et al. On Weakly Commuting Set-Valued Mappings on a Domain of Sets Endowed with Directed Graph. Results Math 71, 1277–1295 (2017). https://doi.org/10.1007/s00025-016-0588-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-016-0588-x

Mathematics Subject Classification

Keywords

Search

Navigation