On an open problem of Kyung Soo Kim
Bancha Panyanak · Fixed Point Theory and Applications · 2015
Abstract We prove a convergence theorem of the Mann iteration scheme for a uniformlyL-Lipschitzian asymptotically demicontractive mapping in a $\operatorname{CAT}(\kappa)$ CAT(κ) space with $\kappa>0$ κ>0 . We also obtain a convergence theorem of the Ishikawa iteration scheme for a uniformlyL-Lipschitzian asymptotically hemicontractive mapping. Our results provide a complete solution to an open problem raised by Kim (Abstr. Appl. Anal. 2013:381715, 2013).