Volume 15, Issue 1 (4-2020)                   IJMSI 2020, 15(1): 111-124 | Back to browse issues page


XML Print


Abstract:  

The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.

Type of Study: Research paper | Subject: General

References
1. A.Abkar, B.S.Choudhury, Fixed point results in partially ordered metric spaces using weak contractive inequalities, Facta Universitatis(NIS), Ser. Math. Inform. Vol. 27, No1 (2012), 1-11.
2. A.A.N.Abdou, Some xed point theorems in modular metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 4381-4387. [DOI:10.22436/jnsa.009.06.78]
3. A.A.N.Abdou, M.A.Khamsi, Fixed point results of pointwise contractions in modular metric spaces, Fixed Point Theory and Applications 2013, 2013:163. [DOI:10.1186/1687-1812-2013-163]
4. M.Abbas, S.Ali, P.Kumam, Common xed points in partially ordered modular function spaces, Journal of Inequalities and Applications 2014, 2014:78. [DOI:10.1186/1029-242X-2014-78]
5. Y.I.Alber, S.Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, new results in operator theory, In: Gohberg, I, Lyubich, Yu (eds.) Advances and Appl., vol. 98, pp. 7{22. Birkhauser Verlag, Basel (1997). [DOI:10.1007/978-3-0348-8910-0_2]
6. M. Beygmohammadi and A. Razani, Two xed-point theorems for mappings satisfying a general contractive condition of integral type in the modular space, International Journal of Mathematics and Mathematical Sciences, Article ID 317107 (2010), 10 pages. [DOI:10.1155/2010/317107]
7. N. Cakic, Z.Kadelbur, S.Radenovic and A. Razani, Common xed point results in cone metric spaces for a family of weakly compatible maps, Advances and Applications in Mathematical Sciences, Vol. 1 Issue 1 (2009), 183-207.
8. V.V.Chistyakov, Metric Modular Spaces-Theory and Applications, Springer International Publishing Switzerland 2015. [DOI:10.1007/978-3-319-25283-4]
9. V.V.Chistyakov, Modular metric spaces, I: Basic concepts, Nonlinear Anal., 72 (2010), 1-14. [DOI:10.1016/j.na.2009.04.057]
10. L.Ciric, A. Razan, S. Radivic and J.S. Ume, Common xed point theorems for families of weakly compatible maps, Computers and Mathematics with Applications, 55 (2008), 2533-2543. [DOI:10.1016/j.camwa.2007.10.009]
11. P.N.Dutta, B.S.Choudhury, A Generalisation of Contraction Principle in Metric Spaces, Fixed Point Theory and Applications. Volume 2008, Article ID 406368, 8 pages. [DOI:10.1155/2008/406368]
12. M.B. Ghaemi and A. Razani, Fixed and periodic points in the probabilistic normed and metric spaces, Chaos, Solitons and Fractals, 28 (2006), 1181-1187. [DOI:10.1016/j.chaos.2005.08.192]
13. J.Harjani, K.Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary di erential equations, Nonlinear Analysis 72 (2010) 11881197. [DOI:10.1016/j.na.2009.08.003]
14. M. Jleli, E. Karapinar and B. Samet, Best Proximity Point Result in Modular Spaces with the Fatou Property, Abstract and Applied Analysis, Volume 2013, Article ID 329451, 4 pages http://dx.doi.org/10.1155/2013/329451. [DOI:10.1155/2013/329451]
15. M.A. Khamsi, Quasicontraction Mappings in Modular Spaces without 2Condition, Fixed Point Theory and Applications, Volume 2008, Article ID 916187, 6 pages doi:10.1155/2008/916187. [DOI:10.1155/2008/916187]
16. M.A.Khamsi, W.M.Kozlowski, Fixed Point Theory in Modular Function Spaces, DOI 10.1007/978-3-319-14051-3, Springer International Publishing Switzerland 2015. [DOI:10.1007/978-3-319-14051-3]
17. C.Mongkolkeha, P.Kumam, Some xed point Results for Generalised Weak Contraction Mappings in Modular Spaces, International Journal of Analysis. Volume 2013, Articlle ID 247378, 6 pages. [DOI:10.1155/2013/247378]
18. M.Ozturk, M.Abbas, E.Girgin, Common xed point results of a pair of generalized contraction mappings in modular spaces, Fixed Point Theory and Applications (2016) 2016:19. [DOI:10.1186/s13663-016-0503-x]
19. A.Padcharoen, D.Gopal, P.Chaipunya and P.Kumam, Fixed point and periodic point results for type F-contractions in modular metric spaces, Fixed Point Theory and Applications (2016), 2016:39 DOI 10.1186/s13663-016-0525-4. [DOI:10.1186/s13663-016-0525-4]
20. A. Razani, A xed point theorem in the Menger probabilistic metric space, New Zealand J. Math., 35 (2006), 109-114.
21. A. Razani, Results in Fixed Point Theory, Andisheh Zarin publisher, Qazvin, August 2010. [DOI:10.1155/2010/476913]
22. A. Razani and M. Shiradaryazdi, Some results on xed points in the fuzzy metric space, J. Appl. Math. Comput., 20 (2006), 401-408. [DOI:10.1007/BF02831947]
23. A. Razani and S. Homaeipour, Viscosity approximation to common xed points of families of nonexpansive mappings with weakly contractive mappings, Fixed Point Theory Applications, Article ID 476913 (2010), 8 pages. [DOI:10.1155/2010/476913]
24. A. Razani and R. Moradi, Common xed point theorems of integral type in modular spaces, Bulletin of the Iranian Mathematical Society, Vol. 35 No. 2 (2009), 11-24.
25. A. Razani and R. Moradi, Double sequence iterations for a strongly contractive mapping in the modular space, Iranian Journal of Mathematical Sciences and Informatics, 11(2016), No. 2, 119-130.
26. A. Razani and V. Parvaneh, Some xed point theorems for weakly T-Chatterjea and weakly T-Kannan-contractive mappings in complete metric spaces, Russian Mathematics (Iz. VUZ), 57 (2013), No.3, 38-45. [DOI:10.3103/S1066369X13030055]
27. A. Razani and V. Parvaneh, On generalized weakly G-contractive mappings in partially ordered G-metric spaces, Abstract and Applied Analysis, Article ID 701910 (2012), 18 pages. [DOI:10.1155/2012/701910]
28. A. Razani and M. Samanipour, Common xed point theorems for families of weakly compatible maps in a 2-metric space, Applied Mathematics and Information Sciences, 2(3) (2008), 275-289.
29. H. R. Sahebi, A. Razani, An explicit viscosity iterative algorithm for nding xed points of two noncommutative nonexpansive mappings, Iranian Journal of Mathematical Sciences and Informatics, 11 (2016), No. 1, 69-83.

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.