Some Fixed-Point Theorems over a Generalized F -Metric Space

Abstract

In this article, the concept of sequential $\mathcal{F}$ -metric spaces has been introduced as a generalization of usual metric spaces, $b$ -metric spaces, $JS$ -metric spaces, and mainly $\mathcal{F}$ -metric spaces. Some topological properties of such spaces have been discussed here. By considering this notion, we prove fixed-point theorems for some classes of contractive mappings over such spaces. Examples have been given in order to examine the validity of the underlying space and in support of our fixed-point theorems. Moreover, our fixed-point theorem is applied to obtain solution of a system of linear algebraic equations.