The Generalized \(\alpha\)-Nonexpansive Mappings and Related Convergence Theorems in Hyperbolic Spaces
Cholatis Suanoom, Kittikorn Sriwichai, Chakkrid Klin-eam, Wongvisarut Khuangsatung · Journal of Informatics and Mathematical Sciences · 2019
In this paper, we propose and analyze a generalized \(\alpha\)-nonexpansive mappings on a nonempty subset of a hyperbolic space i.e., \begin{align*} \frac{1}{2}d(x,Tx)\leq d(x,y)\Longrightarrow d(Tx,Ty)\leq \alpha d(y,Tx)+\alpha d(x,Ty)+ (1-2\alpha)d(x,y), \end{align*} and prove \(\Delta\)-convergence theorems and convergence theorems for a generalized \(\alpha\)-nonexpansive mappings in a hyperbolic space.