Fixed point theorems for Lipschitzian type mappings in \(CAT(0)\) spaces (Q1933916)

The purpose of the paper is to investigate the demiclosedness principle, the existence and iterative approximation for fixed points for nearly asymptotically nonexpansive mappings in the framework of \(CAT(0)\) spaces. The authors prove \(\Delta\)-convergence and strong convergence of the Ishikawa scheme: \[ \begin{aligned} x_{n+1}&=(1-\alpha_n)x_n\bigoplus \alpha_nT^ny_n,\\ y_{n}&=(1-\beta_n)x_n\bigoplus \beta_nT^nx_n, \;n\in \mathbb{N}, \end{aligned} \] where \(\mathbb{N}\) stands for the set of natural numbers, \(\{\alpha_n\}\) and \(\{\beta_n\}\) are real sequences in \((0,1)\), and \(T\) is a nearly asymptotically nonexpansive self-mapping defined on a convex subset of a \(CAT(0)\) space. The present results generalize, extend and unify some recent results in the literature.