A novel approach of graphical rectangular b-metric spaces with an application to the vibrations of a vertical heavy hanging cable

Abstract

In the present article, first, we introduce the notation of graphical rectangular b-metric spaces and scrutinize some basic and topological properties of the underlying spaces. Some examples endowed with appropriate graphs are propounded to validate the established results, thereby giving a better insight into the corresponding concepts and investigations. Our results extend and improve several results in the literature. Second, by means of the obtained results, an application to the vibrations of a vertical heavy hanging cable is entrusted to manifest the viability of the obtained results. Finally, some open problems are also stated for the future scope of the study.