We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by Matkowski to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting.
"Contractibility of Fixed Point Sets of Mean-Type Mappings." Abstr. Appl. Anal. 2017 1 - 7, 2017. https://doi.org/10.1155/2017/3689069