The Generalized \(α\)-Nonexpansive Mappings and Related Convergence Theorems in Hyperbolic Spaces (Journal of Informatics and Mathematical Sciences, 2019)
In this paper, we propose and analyze a generalized \(α\)-nonexpansive mappings on a nonempty subset of a hyperbolic space i.e., \begin{align*} \frac{1}{2}d(x,Tx)≤ d(x,y)\Longrightarrow d(Tx,Ty)≤ α d(y,Tx)+α d(x,Ty)+ (1-2α)d(x,y), \end{align*} and prove \(Δ\)-convergence theorems and convergence theorems for a generalized \(α\)-nonexpansive mappings in a hyperbolic space.
Keywords: Fixed point set; Generalized \(α\)-nonexpansive mappings; \(Δ\)-convergence theorems and hyperbolic spaces