Some Applications of the Weak Contraction Principle (Letters in Nonlinear Analysis and its Applications, 2025)
Recently we obtained several extensions of the Banach contraction principle. One of them is the weak contraction principle or the Rus-Hicks-Rhoades contraction principle or Theorem P. There are a large number of examples or applications of Theorem P in the literature. Recently, Romaguera stated two corollaries of Theorem P are false. Our main aim of this paper is to clarify his claim
Keywords: fixed point; quasi-metric; Rus-Hicks-Rhoades (RHR) map; T-orbitally complete