A relation theoretic <i>m</i>-metric fixed point algorithm and related applications

Abstract

&lt;abstract&gt;&lt;p&gt;In this article, we introduce the concept of generalized rational type $ F $ -contractions on relation theoretic &lt;italic&gt;m&lt;/italic&gt;-metric spaces (denoted as $ F_{R}^{m} $-contractions, where $ R $ is a binary relation) and some related fixed point theorems are provided. Then, we achieve some fixed point results for cyclic rational type $ F_{R}^{m} $- generalized contraction mappings. Moreover, we state some illustrative numerically examples to show our results are true and meaningful. As an application, we discuss a positive definite solution of a nonlinear matrix equation of the form $ \Lambda = S+\sum\limits_{i = 1}^{\mu }Q_{i}^{\ast }\Xi \left(\Lambda \right) Q_{i} $.&lt;/p&gt;&lt;/abstract&gt;