- Universal Journal of Mathematics and Applications
- Vol: 2 Issue: 2
- Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equatio...
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 : 9 | Download : 3
Publication Date : 2019-06-28
Article Type : Research
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 $(alpha, eta )$-admissible mapping, $(alpha, eta )-(psi, phi )$-contractive mapping