### Fixed Point Theorems of \(\alpha_*\)-\(\psi\)-Common Rational Type Contractive Order Closed Set-Valued Mappings on Generalized Metric Spaces

#### Abstract

Alsulami *et al*. [4] introduced the notion of \((\alpha\)-\(\psi)\)-rational type contractive mappings. They have been established some fixed point theorems for the mappings in complete generalized metric spaces. In this paper, we introduce the notion of some fixed point theorems of \(\alpha_*\)-\(\psi\)-common rational type contractive order closed set-valued mappings on generalized metric spaces with application to fractional integral equations and give a common fixed point result about fixed points of the set-valued mappings.\ Also, we give a result about common fixed points of self-maps on a partially ordered set and on complete metric satisfy a contractive condition.

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DOI: http://dx.doi.org/10.26713%2Fjims.v12i4.1492

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