A New Fixed Point Theorem in Modular Metric Spaces

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Ali Mutlu, Kubra Ozkan, Utku Gurdal, A New Fixed Point Theorem in Modular Metric Spaces, Int. J. Anal. Appl., 16 (4) (2018), 472-483.

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Ali Mutlu, Kubra Ozkan, Utku Gurdal

Abstract

In this article, we first give a new fixed point theorem which is main theorem of our study in modular metric spaces. After that, by using this theorem, we express some interesting results. Moreover, we characterize completeness in modular metric spaces via this theorem. Finally, we use our main result to show the existence of solution for a specific problem in dynamic programming.

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References

  1. O. Acar and I. Altun, Some generalizations of Caristi type fixed point theorem on partial metric spaces, Filomat, 26(4) (2012), 833-837.
  2. H. Aydi and M. Abbas, Tripled coincidence and fixed point results in partial metric spaces, Appl. Gen. Topol., 13(2) (2012), 193-206.
  3. A.A.N. Abdou and M.A. Khamsi, Fixed point results of pointwise contractions in modular metric spaces, Fixed Point Theory Appl., 2013 (2013), Article ID 163.
  4. A.A.N. Abdou and M.A. Khamsi, Fixed points of multivalued contraction mappings in modular metric spaces, Fixed Point Theory Appl., 2014 (2014), Article ID 249.
  5. C. Alaca, M.E. Ege and C. Park, Fixed point results for modular ultrametric spaces, J. Comput. Anal. Appl., 20(1) (2016), 1259-1267.
  6. S. Banach, Sur les op ´ erations dans les ensembles abstraits et leur application aux ´ equations int ´ egrales, Fund. Math., 3 (1922), 133-181.
  7. T.G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393.
  8. J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Am. Math. Soc., 215 (1976), 241-251.
  9. V.V. Chistyakov, Modular metric spaces generated by F-modulars, Folia Math., 14 (2008), 3-25.
  10. V.V. Chistyakov, Modular metric spaces, I: basic concepts, Nonlinear Anal., 72 (2010), 1-14.
  11. V.V. Chistyakov, Fixed points of modular contractive maps, Doklady Math., 86(1) (2012), 515-518.
  12. Y.J. Cho, R. Saadati and G. Sadeghi, Quasi-contractive mappings in modular metric spaces, J. Appl. Math., 2012 (2012), 907-951.
  13. I. Erhan, E. Karapinar and D. Turkoglu, Different types Meir-Keeler contractions on partial metric, J. Comput. Anal. Appl, 14 (2012), 1000-1005.
  14. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
  15. M.A. Khamsi, Remarks on Caristi's fixed point theorem, Nonlinear Anal., 71(1-2) (2009), 227-231.
  16. W.A. Kirk, Caristi's fixed point theorem and metric convexity, Colloq. Math., 36 (1976), 81-86.
  17. P. Kumam, Fixed point theorems for nonexpansive mapping in modular spaces, Arch. Math., 40 (2004), 345-353.
  18. C. Mongkolkeha, W. Sintunavarat and P. Kumam, Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory Appl., 2011 (2011), Article ID 93.
  19. A. Mutlu, K. ¨ Ozkan and U. Gürdal, Coupled fixed point theorems on bipolar metric spaces, Eur. J. Pure Appl. Math., 10(4) (2017), 655-667.
  20. A. Mutlu, K. ¨ Ozkan and U. Gürdal, Coupled fixed point theorem in partially ordered modular metric spaces and its an application, J. Comput. Anal. Appl., 25(2) (2018), 1-10.
  21. H. Nakano, Modulared Semi-Ordered Linear Spaces, In Tokyo Math. Book Ser., 1, Maruzen Co. Tokyo, 1950.
  22. J. Musielak and W. Orlicz, On modular spaces, Studia Math., 18 (1959), 49-65.
  23. W. Shatanawi, B. Samet and M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Model., 55(3-4) (2012), 680-687.
  24. T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317.