In this article, we introduce the concept of generalized rational type F-contractions on relation theoretic m-metric spaces (denoted as FRm-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 FRm-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 (Formula presented).
- generalized rational type FR-contractions
- matrix equation
- relation theoretic m-metric