A History of Contraction Principles
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Keywords:
fixed point, quasi-metric, Rus-Hicks-Rhoades (RHR) map, T-orbitally complete.Abstract
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 wellknown theorems of Banach, Covitz-Nadler, Oettli-Thera, Rus-Hicks-Rhoades, and some others.
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