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 : 14 | Download : 10

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