Computational and Applied Mathematics

, Volume 36, Issue 4, pp 1607–1622 | Cite as

Common fixed points of set-valued F-contraction mappings on domain of sets endowed with directed graph

  • Mujahid Abbas
  • Talat Nazir
  • Tatjana Aleksić Lampert
  • Stojan Radenović


The aim of this paper is to present common fixed point results of set-valued graphic F-contraction mappings on a family of sets endowed with a graph. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.


Set-valued mapping Domain of sets Common fixed point Graph F-contraction pair Directed graph 

Mathematics Subject Classification

47H10 54E50 54H25 


  1. Abbas M, Alfuraidan MR, Khan AR, Nazir T (2015) Fixed point results for set-contractions on metric spaces with a directed graph. Fixed Point Theory Appl 14:1–9MATHGoogle Scholar
  2. Abbas M, Alfuraidan MR, Nazir T (2016) Common fixed points of multivalued \(F\)-contractions on metric spaces with a directed graph. Carpath. J. Math. 32(1):1–12MATHGoogle Scholar
  3. Abbas M, Ali B, Petrusel G (2014) Fixed points of set-valued contractions in partial metric spaces endowed with a graph. Carpath. J. Math. 30(2):129–137MATHGoogle Scholar
  4. Abbas M, Nazir T (2013) Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph. Fixed Point Theory Appl 20:1–8MATHGoogle Scholar
  5. Aleomraninejad SMA, Rezapoura Sh, Shahzad N (2012) Some fixed point results on a metric space with a graph. Topol Appl 159:659–663CrossRefMATHGoogle Scholar
  6. Alfuraidan MR, Khamsi MA (2014) Caristi fixed point theorem in metric spaces with a graph. Abstr Appl Anal 1–5 (Article ID 303484)Google Scholar
  7. Amini-Harandi A, Emami H (2010) A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations. Nonlinear Anal 72:2238–2242CrossRefMATHGoogle Scholar
  8. Assad NA, Kirk WA (1972) Fixed point theorems for setvalued mappings of contractive type. Pacific J Math 43:533–562CrossRefGoogle Scholar
  9. Beg I, Butt AR (2013) Fixed point theorems for set valued mappings in partially ordered metric spaces. Int J Math Sci 7(2):66–68Google Scholar
  10. Beg I, Butt AR (2013) Fixed point of set-valued graph contractive mappings, J Inequ Appl 52:7Google Scholar
  11. Berinde M, Berinde V (2007) On a general class of multivalued weakly Picard mappings. J Math Anal Appl 326:772–782CrossRefMATHGoogle Scholar
  12. Berinde V (2007) Iterative approximation of fixed points. Springer-Verlag, Berlin-HeidelbergMATHGoogle Scholar
  13. Bojor F (2010) Fixed point of \(\varphi \)-contraction in metric spaces endowed with a graph. Ann Univ Craiova Math Comp Sci Series 37(4):85–92Google Scholar
  14. Bojor F (2012) Fixed point theorems for Reich type contractions on metric spaces with a graph. Nonlinear Anal 75:3895–3901CrossRefMATHGoogle Scholar
  15. Bojor F (2012) On Jachymski’s theorem. Ann Univ Craiova Math Comp Sci Series 40(1):23–28Google Scholar
  16. Chifu CI, Petrusel GR (2012) Generalized contractions in metric spaces endowed with a graph. Fixed Point Theory Appl 161:1–9MATHGoogle Scholar
  17. Edelstein M (1961) An extension of Banach’s contraction principle. Proc Am Math Soc 12:7–10MATHGoogle Scholar
  18. Gwozdz-Lukawska G, Jachymski J (2009) IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem. J Math Anal Appl 356:453–463CrossRefMATHGoogle Scholar
  19. Harjani J, Sadarangani K (2009) Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Anal 71:3403–3410CrossRefMATHGoogle Scholar
  20. Jachymski J, Jozwik I (2007) Nonlinear contractive conditions: a comparison and related problems. Banach Center Publ 77:123–146CrossRefMATHGoogle Scholar
  21. Jachymski J (2008) The contraction principle for mappings on a metric space with a graph. Proc Am Math Soc 136:1359–1373CrossRefMATHGoogle Scholar
  22. Nadler SB (1969) Multivalued contraction mappings. Pacific J Math 30:475–488CrossRefMATHGoogle Scholar
  23. Nieto JJ, López RR (2005) Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22:223–239CrossRefMATHGoogle Scholar
  24. Nicolae A, O’Regan D, Petrusel A (2011) Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph. J Georgian Math Soc 18:307–327MATHGoogle Scholar
  25. Ran ACM, Reurings MCB (2004) A fixed point theorem in partially ordered sets and some application to matrix equations. Proc Am Math Soc 132:1435–1443CrossRefMATHGoogle Scholar
  26. Sgroi M, Vetro C (2013) Multi-valued \(F\)-contractions and the solution of certain functional and integral equations. Filomat 27(7):1259–1268CrossRefMATHGoogle Scholar
  27. Shukla S, Radenović S (2013) Some common fixed point theorems for \(F\)-complete partial metric spaces. J Math 2013(Article ID 878730):7Google Scholar
  28. Shukla S, Radenović S, Kadelburg Z (2014) Some fixed point theorems for ordered \(F\)-generalized contractions in 0-f-orbitally complete partial metric spaces. Theor Appl Math Comput Sci 4(1):87–98MATHGoogle Scholar
  29. Wardowski D (2012) Fixed points of new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl 94:1–6MATHGoogle Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016

Authors and Affiliations

  • Mujahid Abbas
    • 1
    • 2
  • Talat Nazir
    • 3
    • 4
  • Tatjana Aleksić Lampert
    • 5
  • Stojan Radenović
    • 6
  1. 1.Nonlinear Analysis Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Division of Applied Mathematics, School of Education, Culture and CommunicationMälardalen UniversityVästeråsSweden
  4. 4.Department of MathematicsCOMSATS Institute of Information TechnologyAbbottabadPakistan
  5. 5.Faculty of Sciences, Department of MathematicsKragujevacSerbia
  6. 6.Department of Mathematical SciencesState University of Novi PazarNovi PazarSerbia

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