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

Year 2019, Volume: 2 Issue: 2, 85 - 93, 28.06.2019

Müzeyyen Sangurlu Sezen

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

Cited By: 3

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

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