(φ, ψ)-Contractıon Condition for Multivalued Mappings in Complete Modular Metric Spaces

Main Article Content

Duran Turkoglu
Emine Kilinc

Abstract

In this paper we investigated (φ, ψ)-contractıon condition for multivalued type mappings in complete modular metric spaces. Our results are more general than metric versions of these type mappings.

Keywords:
fixed point, Modular metric spaces, Hausdorff metric.

Article Details

How to Cite
Turkoglu, D., & Kilinc, E. (2020). (φ, ψ)-Contractıon Condition for Multivalued Mappings in Complete Modular Metric Spaces. Asian Research Journal of Mathematics, 16(11), 54-61. https://doi.org/10.9734/arjom/2020/v16i1130242
Section
Original Research Article

References

Banach S. Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales. Fund. Math. 1922;3:133-181.

Rakotch A. A note on contraction mappings. Proc. Amer. Math. Soc. 1962;13:459-462.

Boyd DW, Wong TS. On nonlinar contractions. Proc. Amer. Math. Soc. 1969;20:458-464.

Rhoades BH. Some theorem on weakly contraction maps. Nonlinear Anal. 2001;47:2683-2693.

Zang Q, Song Y. Fixed point theory for generalized ψ−weak contractions. Applied Mathematics Letters. 2009;22:75-78.

Doric D. Common fixed point for generalized (ψ, φ) −weak contractions. Applied Mathematics Letters. 2009;22:1896-1900.

Hosseini VR. Common fixed point for generalized (ψ, φ) −weak contraction mappings condition of integral type. Int. J. of Math. Anal. 2010;4(31):1535-1543.

Nadler Jr. SB. Multi-valued contraction mappings. Pasific J. Math. 1969;30:475-487.

Nakano H. Modulared semi-ordered linear space. In Tokyo Math. Book Ser, Maruzen Co, Tokyo. 1950;1.

Koshi S, Shimogaki T. On F-norms of quasi-modular space. J. Fac. Sci. Hokkaido Univ. Ser 1. 1961;15(3-4):202-218. 60Turkoglu and Kilinc; ARJOM, 16(11): 54-61, 2020; Article no.ARJOM.64013

Yamammuro S. On conjugate space of Nakano Space. Trans. Amer. Math. Soc. 1959;90:291- 311.

Musielakand J, Orlicz W. On modular spaces. Studia Math. 1959;18:49-65.

Chistyakov VV. Metric modulars and their application. Dokl. Akad. Nauk. 2006;406(2):165- 168.

Chistyakov VV. Modular metric spaces generated by F-modulars. Folia Math. 2008;14:3-25.

Chistyakov VV. Modular metric spaces I. basic conceps. Nonlinear Anal. 2010;72:1-14.

Chistyakov VV. A fixed poin theorem for contractions in modular metric spaces; 2011. ArXiv e-prints

Azadifar B, Maramaei M, Sadeghi GH. Common fixed point theorems in modular G-metric spaces. Journal Nonlinear Analysis and Application. 2013;2013:1-9.

Chaipunya P, Cho YJ, Kumam P. Geraghty-type theorems in modular metric spaces with an application to partial differential equation. Advances in Difference Equations. 2012;2012:83. DOI:10.1186/1687-1847-2012-83

Cho YJ, Saadati R, Sadeghi GH. Quasi-contractive mappings in modular metric spaces. Journal of Applied Mathematics. 2012;5. Article ID 907951 DOI:10.1155/2012/907951

Dehghan H, Eshaghi Gordji M, Ebadian A. Comment on ’Fixed point theorems for contraction mappings in modular metric spaces. Fixed Point Theory and Applications. 2012;2012:144. DOI:10.1186/1687-1812-2011-93

Mongkolkeha C, Sintunavarat W, Kumam P. Fixed point theorems for contraction mappings in modular metric spaces. Fixed Point Theory and Applications; 2011. DOI:10.1186/1687-1812-2011-93

Azadifar B, Sadeghi GH, Saadati R, Park C. Integral type contractions in modular metric spaces. Journal of Inequalities and Applications. 2013;2013:483. DOI:10.1186/1029-242X-2013-483

Kılın¸c E, Alaca C. A fixed point theorem in modular metric spaces. Advances in Fixed Point Theory. 2014;4(2):199-206.

Kılın¸c E, Alaca C. Fixed point results for commuting mappings in modular metric spaces. Journal of Applied Functional Analysis. 2015;10:204-210.

Afrah AN Abdou, Khamsi M. Fixed points of multivalued contraction mappings in modular metric spaces. Fixed Point Theory and Applications. 2014;2014:249.

Chaipunya P, et al. Fixed-point theorems for multivalued mappings in modular metric spaces. Abstract and Applied Analysis; 2012. Hindawi Publishing Corporation; 2012.

Turkoglu D, Kilinc E. Some fixed point results for caristi type mappings in modular metric spaces with an application. International Journal of Analysis and Applications. 2016;12(1):15- 21.