Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations
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...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2019-06-01
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| Series: | Universal Journal of Mathematics and Applications |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/747081 |
| _version_ | 1797350196385939456 |
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| author | Müzeyyen Sangurlu Sezen |
| author_facet | Müzeyyen Sangurlu Sezen |
| author_sort | Müzeyyen Sangurlu Sezen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T12:41:16Z |
| format | Article |
| id | doaj.art-4fb09fe70af444d7b534de24eecc3398 |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:16Z |
| publishDate | 2019-06-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-4fb09fe70af444d7b534de24eecc33982024-01-21T10:08:38ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532019-06-0122859310.32323/ujma.5438241225Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral EquationsMüzeyyen Sangurlu Sezen0Giresun UniversityThe 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.https://dergipark.org.tr/tr/download/article-file/747081modular spacecyclic $(\alpha ;\beta )$-admissible mapping$(\alpha ;\beta )-(\psi ;\phi )$-contractive mapping |
| spellingShingle | Müzeyyen Sangurlu Sezen Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations Universal Journal of Mathematics and Applications modular space cyclic $(\alpha ;\beta )$-admissible mapping $(\alpha ;\beta )-(\psi ;\phi )$-contractive mapping |
| title | Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations |
| title_full | Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations |
| title_fullStr | Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations |
| title_full_unstemmed | Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations |
| title_short | Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations |
| title_sort | cyclic alpha beta admissible mappings in modular spaces and applications to integral equations |
| topic | modular space cyclic $(\alpha ;\beta )$-admissible mapping $(\alpha ;\beta )-(\psi ;\phi )$-contractive mapping |
| url | https://dergipark.org.tr/tr/download/article-file/747081 |
| work_keys_str_mv | AT muzeyyensangurlusezen cyclicalphabetaadmissiblemappingsinmodularspacesandapplicationstointegralequations |