Glasnik Matematicki, Vol. 52, No. 1 (2017), 163-177.

COMMON FIXED POINT THEOREMS FOR A FAMILY OF MULTIVALUED F-CONTRACTIONS WITH AN APPLICATION TO SOLVE A SYSTEM OF INTEGRAL EQUATIONS

Tayyab Kamran, Fahimuddin and Muhammad Usman Ali

Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
& Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan
e-mail: tayyabkamran@gmail.com

Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
e-mail: fahamiiu@gmail.com

Department of Mathematics, COMSATS Institute of Information Technology, Attock, Pakistan
e-mail: muh_usman_ali@yahoo.com


Abstract.   Inspired by the work of Wardowski in [33] and Samet et al. in [26], in this article, we introduce some new contractive conditions for sequence of multi functions. We have constructed non-trivial examples to validate our results. We have applied our results to find a solution of a system of integral equations.

2010 Mathematics Subject Classification.   47H10, 54H25.

Key words and phrases.   α-admissible sequences, α*-admissible sequences, F-contractions.


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DOI: 10.3336/gm.52.1.12


References:

  1. O. Acar and I. Altun, A fixed point theorem for multivalued mappings with δ-distance, Abstr. Appl. Anal. 2014, Art. ID 497092, 5 pp.
    MathSciNet     CrossRef

  2. M. U. Ali, T. Kamran and E. Karapinar, Further discussion on modified multivalued α*-ψ- contractive type mapping, Filomat 29 (2015), 1893-1900.
    MathSciNet     CrossRef

  3. M. U. Ali, T. Kamran and E. Karapinar, A new approach to (α,ψ)-contractive nonself multivalued mappings, J. Inequal. Appl. 2014, 2014:71, 9 pp.
    MathSciNet     CrossRef

  4. M. U. Ali, Q. Kiran and N. Shahzad, Fixed point theorems for multivalued mappings involving α-function, Abstr. Appl. Anal. 2014, Art. ID 409467, 6pp.
    MathSciNet     CrossRef

  5. M. U. Ali, T. Kamran and N. Shahzad, Best proximity point for α-ψ-proximal contractive multimaps, Abstr. Appl. Anal. 2014, Art. ID 181598, 6pp.
    MathSciNet     CrossRef

  6. M. U. Ali and T. Kamran, On *,ψ)-contractive multi-valued mappings, Fixed Point Theory Appl. 2013, 2013:137, 7pp.
    MathSciNet     CrossRef

  7. J. H. Asl, S. Rezapour and N. Shahzad, On fixed points of α-ψ-contractive multifunctions, Fixed Point Theory Appl. 2012, 2012:212, 6pp.
    MathSciNet     CrossRef

  8. H. Aydi, E. Karapinar and B. Samet, Fixed points for generalized (α,ψ)-contractions on generalized metric spaces, J. Inequal. Appl. 2014, 2014:229, 16pp.
    MathSciNet     CrossRef

  9. R. Batra and S. Vashistha, Fixed points of an F-contraction on metric spaces with a graph, Int. J. Comput. Math. 91 (2014), 2483-2490.
    MathSciNet     CrossRef

  10. M. Berinde and V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. 326 (2007), 772-782.
    MathSciNet     CrossRef

  11. F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. Stiint. Univ. "Ovidius'' Constanta Ser. Mat. 20 (2012), 31-40.
    MathSciNet    

  12. S. H. Cho, Fixed point theorems for α-ψ-contractive type mappings in metric spaces, Appl. Math. Sci. (Ruse) 7 (2013), 6765-6778.
    MathSciNet     CrossRef

  13. M. Cosentino and P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat 28 (2014), 715-722.
    MathSciNet     CrossRef

  14. Y. Feng and S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006), 103-112.
    MathSciNet     CrossRef

  15. E. Karapinar, Discussion on (α,ψ) contractions on generalized metric spaces, Abstr. Appl. Anal. 2014, Art. ID 962784, 7pp.
    MathSciNet     CrossRef

  16. E. Karapinar and B. Samet, Generalized α-ψ-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012, Art. ID 793486.
    MathSciNet    

  17. E. Karapinar and R. P. Agarwal, A note on 'Coupled fixed point theorems for α-ψ-contractive-type mappings in partially ordered metric spaces', Fixed Point Theory Appl. 2013, 2013:216, 16pp.
    MathSciNet     CrossRef

  18. M. A. Miandaragh, M. Postolache and Sh. Rezapour, Some approximate fixed point results for generalized α-contractive mappings, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 75 (2013), 3-10.
    MathSciNet    

  19. G. Minak and I. Altun, Some new generalizations of Mizoguchi-Takahashi type fixed point theorem, J. Inequal. Appl. 2013, 2013:493, 10pp.
    MathSciNet     CrossRef

  20. G. Minak, A. Helvaci and I. Altun, Ćirić type generalized F-contractions on complete metric spaces and fixed point results, Filomat 28 (2014), 1143-1151.
    MathSciNet     CrossRef

  21. B. Mohammadi, S. Rezapour and N Shahzad, Some results on fixed points of α-ψ-Ciric generalized multifunctions, Fixed Point Theory Appl. 2013, 2013:24, 10pp.
    MathSciNet     CrossRef

  22. D. Paesano and C. Vetro, Multi-valued F-contractions in 0-complete partial metric spaces with application to Volterra type integral equation, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 108 (2014), 1005-1020.
    MathSciNet     CrossRef

  23. H. K. Pathak and N. Shahzad, Fixed point results for set-valued contractions by altering distances in complete metric spaces, Nonlinear Anal. 70 (2009), 2634-2641.
    MathSciNet     CrossRef

  24. H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl. 2014, 2014:210, 11pp.
    MathSciNet     CrossRef

  25. D. O'Regan and A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008), 1241-1252.
    MathSciNet     CrossRef

  26. B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.
    MathSciNet     CrossRef

  27. P. Salimi, A. Latif and N. Hussain, Modified α-ψ-contractive mappings with applications, Fixed Point Theory Appl. 2013, 2013:151, 19pp.
    MathSciNet     CrossRef

  28. N.-A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. 2013, 2013:277, 13pp.
    MathSciNet     CrossRef

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

  30. W. Shatanawi and M. Postolache, Some fixed point results for a G-weak contraction in G-metric spaces, Abstr. Appl. Anal. 2012, Art. ID 815870, 19 pp.
    MathSciNet    

  31. T. Sistani and M. Kazemipour, Fixed point theorems for α-ψ-contractions on metric spaces with a graph, J. Adv. Math. Stud. 7 (2014), 65-79.
    MathSciNet    

  32. S. L. Singh, S. N. Mishra and S. Jain, Round-off stability for multi-valued maps, Fixed Point Theory Appl. 2012, 2012:12, 10pp.
    MathSciNet     CrossRef

  33. D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 2012:94, 6pp.
    MathSciNet     CrossRef

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