- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 7 Issue: 2
- Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces
Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces
Authors : Sehie PARK
Pages : 455-472
Doi:10.31197/atnaa.1185449
View : 21 | Download : 38
Publication Date : 2023-07-23
Article Type : Research Article
Abstract :Let $(X, d)$ be a quasi-metric space. A Rus-Hicks-Rhoades (RHR) map $f : X \\to X$ is the one satisfying $d(fx, f^2x) \\le \\alpha d(x, fx)$ for every $x\\in X$, where $\\alpha \\in [0,1)$. In our previous work [37], we collected various fixed-point theorems closely related to RHR maps. In the present article, we collect almost all the things we know about RHR maps and their examples. Moreover, we derive new classes of generalized RHR maps and fixed point theorems on them. Consequently, many of the known results in metric fixed point theory are improved and reproved in an easy way.Keywords : fixed point theorem, metric space, fixed point, stationary point, maximal element