A History of Contraction Principles

Recently we obtained several extensions of the Banach contraction principle, which appears frequently in many literature.From our 2023 Metatheorem, we deduce Theorem H on the equivalent formulations of completeness of quasi-metric spaces.From Theorem H, we derive the Banach contraction principle, its extended form (Theorem Q), the Rus-Hicks-Rhoades contraction principle (Theorem P), and others.Consequently, our Theorem H contains well-known theorems of Banach, Covitz-Nadler, Oettli-Thra, Rus-Hicks-Rhoades, and some others.