- Universal Journal of Mathematics and Applications
- Volume:2 Issue:2
- Cyclic $(alpha ,beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations
Cyclic $(alpha ,beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations
Authors : Müzeyyen SANGURLU SEZEN
Pages : 85-93
Doi:10.32323/ujma.543824
View : 50 | Download : 11
Publication Date : 2019-06-28
Article Type : Research Paper
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 $insert ignore into journalissuearticles values(\alpha ,\beta );-insert ignore into journalissuearticles values(\psi ,\varphi );-$ 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, eta, admissible mapping, alpha, eta, psi, phi, contractive mapping
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