Glasnik Matematicki, Vol. 52, No. 1 (2017), 147-161.

A SUZUKI FIXED POINT THEOREM FOR GENERALIZED MULTIVALUED MAPPINGS ON METRIC-LIKE SPACES

Hassen Aydi, Abdelbasset Felhi and Slah Sahmim

Department of Mathematics and Statistics, King Faisal University, College of Sciences, 31928 Al Ahsaa, Saudi Arabia
e-mail: afelhi@kfu.edu.sa
e-mail: ssahmim@kfu.edu.sa

Abstract.   Based on a new papers of Aydi et al. in [7, 8], where the concept of Hausdorff metric-like has been initiated, we introduce Suzuki type contractive multivalued mappings on metric-like spaces. We also establish several fixed point results involving such contractions. We show that many known fixed point results in literature are simple consequences of our theorems. Our obtained results are supported by some examples and an application.

2010 Mathematics Subject Classification.   47H10, 54H25.

Key words and phrases.   Hausdorff metric-like, multi-valued mapping, fixed point.

DOI: 10.3336/gm.52.1.11

References:

1. C. T. Aage and J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci. (Ruse) 2 (2008), 2941-2948.
   MathSciNet    

2. M. Abbas, B. Ali and C. Vetro, A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topology Appl. 160 (2013), 553-563.
   MathSciNet     CrossRef

3. A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012, 2012:204, 10pp.
   MathSciNet     CrossRef

4. H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl. 159 (2012), 3234-3242.
   MathSciNet     CrossRef

5. H. Aydi, M. Abbas and C. Vetro, Common fixed points for multivalued generalized contractions on partial metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 108 (2014), 483-501.
   MathSciNet     CrossRef

6. H. Aydi and A. Felhi, On best proximity points for various α-proximal contractions on metric-like spaces, J. Nonlinear Sci. Appl. 9 (2016), 5202-5218.
   MathSciNet    

7. H. Aydi, A. Felhi, E. Karapinar and S. Sahmim, Hausdorff metric-like, generalized Nadler's fixed point theorem on metric-like spaces and application, Miskolc Math. Notes, in press.

8. H. Aydi, A. Felhi and S. Sahmim, Fixed points of multivalued nonself almost contractions in metric-like spaces, Math. Sci. (Springer) 9 (2015), 103-108.
   MathSciNet     CrossRef

9. H. Aydi and E. Karapinar, Fixed point results for generalized α-ψ-contractions in metric-like spaces and applications, Electron. J. Differential Equations 2015, No. 133, 15pp.
   MathSciNet    

10. R. D. Daheriya, R. Jain and M. Ughade, Some fixed point theorem for expansive type mapping in dislocated metric space, ISRN Math. Anal. 2012, Art. ID 376832, 5 pp.
    MathSciNet    

11. R. George, R. Rajagopalan and S. Vinayagam Cyclic contractions and fixed points in dislocated metric spaces, Int. J. Math. Anal. (Ruse) 7 (2013), 403-411.
    MathSciNet     CrossRef

12. A. Isufati, Fixed point theorems in dislocated quasi-metric space, Appl. Math. Sci. (ruse) 4 (2010), 217-233.
    MathSciNet    

13. E. Karap\i nar and P. Salimi, Dislocated metric space to metric spaces with some fixed point theorems, Fixed Point Theory Appl. 2013 (2013).
    MathSciNet     CrossRef

14. P. S. Kumari, W. Kumar and I. R. Sarma, Common fixed point theorems on weakly compatible maps on dislocated metric spaces, Math. Sci. (Springer) 6 (2012), Art. 71, 5pp.
    MathSciNet     CrossRef

15. P. S. Kumari Some fixed point theorems in generalized dislocated metric spaces, Math. Theory Model. 1 (2011), 4, 16-22.

16. S. G. Matthews, Partial metric topology, in Proceedings of the 8th Summer Conference on General Topology and Applications. Annals of the New York Academy of Sciences 728, 1994, 183-197
    MathSciNet     CrossRef

17. S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488.
    MathSciNet     CrossRef

18. I. R. Sarma and P. S. Kumari, On dislocated metric spaces, Int. J. Math. Arch. 3 (2012), 1, 72-77.

19. R. Shrivastava, Z. K. Ansari and M. Sharma, Some results on fixed points in dislocated and dislocated quasi-metric spaces, J. Adv. Stud. Topol. 3 (2012), 25-31.
    MathSciNet     CrossRef

20. M. Shrivastava, K. Qureshi and A. D. Singh, A fixed point theorem for continuous mapping in dislocated quasi-metric spaces, Int. J. Theor. Appl. Sci. 4 (2012), 1, 39-40.

21. K. Zoto, E. Hoxha and A. Isufati Some new results in dislocated and dislocated quasi-metric spaces, Appl. Math. Sci. (Ruse) 6 (2012), 3519-3526.
    MathSciNet