An Extended b -Metric-Type Space and Related Fixed Point Theorems with an Application to Nonlinear Integral Equations

Abstract

In this paper, the concept of sequential $p$ -metric spaces has been introduced as a generalization of usual metric spaces, $b$ -metric spaces and specially of $p$ -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems.