A Careful Retrospection of Metric Spaces and Contraction Mappings with Computer Simulation

This chapter aims to provide a straightforward layout of the work done on contraction mappings, that play an indispensable role in the fixed-point theory. We aim to display the famous inequalities employing some nontrivial examples using computer simulations. It will help the readers to spot and locate those inequalities that seem to be somewhat abstract. We encapsulate a detailed discussion on the work done in this direction with novel examples. In brief, we also summarize some preliminary and contemporary work done on the generalization of metric spaces and discuss the topology and metrization of some notable metric spaces.