Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations

Müzeyyen Sangurlu Sezen

doi:10.32323/ujma.543824

EN

Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations

Abstract

The main concern of this study is to present a generalization of Banach's fixed point theorem in some classes of modular spaces, where the modular is convex and satisfying the $\Delta _{2}$-condition. In this work, the existence and uniqueness of fixed point for $(\alpha ,\beta )-(\psi ,\varphi )-$ contractive mapping and $\alpha -\beta -\psi -$weak rational contraction in modular spaces are proved. Some examples are supplied to support the usability of our results. As an application, the existence of a solution for an integral equation of Lipschitz type in a Musielak-Orlicz space is presented.

Keywords

Modular space,Cyclic $(\alpha ;\beta )$-admissible mapping,$(\alpha ;\beta )-(\psi ;\phi )$-contractive mapping

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Müzeyyen Sangurlu Sezen ^*
0000-0001-7520-6255
Türkiye

Publication Date

June 28, 2019

Submission Date

March 23, 2019

Acceptance Date

May 3, 2019

Published in Issue

Year 2019 Volume: 2 Number: 2

DOI

https://doi.org/10.32323/ujma.543824

IZ

https://izlik.org/JA76GF64DN

APA

Sangurlu Sezen, M. (2019). Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations. Universal Journal of Mathematics and Applications, 2(2), 85-93. https://doi.org/10.32323/ujma.543824

AMA

1.Sangurlu Sezen M. Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations. Univ. J. Math. Appl. 2019;2(2):85-93. doi:10.32323/ujma.543824

Chicago

Sangurlu Sezen, Müzeyyen. 2019. “Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations”. Universal Journal of Mathematics and Applications 2 (2): 85-93. https://doi.org/10.32323/ujma.543824.

EndNote

Sangurlu Sezen M (June 1, 2019) Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations. Universal Journal of Mathematics and Applications 2 2 85–93.

IEEE

[1]M. Sangurlu Sezen, “Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations”, Univ. J. Math. Appl., vol. 2, no. 2, pp. 85–93, June 2019, doi: 10.32323/ujma.543824.

ISNAD

Sangurlu Sezen, Müzeyyen. “Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations”. Universal Journal of Mathematics and Applications 2/2 (June 1, 2019): 85-93. https://doi.org/10.32323/ujma.543824.

JAMA

1.Sangurlu Sezen M. Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations. Univ. J. Math. Appl. 2019;2:85–93.

MLA

Sangurlu Sezen, Müzeyyen. “Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations”. Universal Journal of Mathematics and Applications, vol. 2, no. 2, June 2019, pp. 85-93, doi:10.32323/ujma.543824.

Vancouver

1.Müzeyyen Sangurlu Sezen. Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations. Univ. J. Math. Appl. 2019 Jun. 1;2(2):85-93. doi:10.32323/ujma.543824