Discussions on Proinov- C b -Contraction Mapping on b -Metric Space

Abstract

In the present paper, we introduce the notion of Proinov- ${\mathcal{C}}_b$ -contraction mapping and we discuss it within the most interesting abstract structure, namely, $b$ -metric spaces. We further take into consideration the necessary conditions to guarantee the existence and uniqueness of fixed points for such mappings, as well as indicate the validity of the main results by providing illustrative examples.