Attractive Point and Mean Convergence Theorems for New Generalized Nonspreading Mappings in Banach Spaces

In this paper, we first introduce a class of nonlinear mappings called generic generalized nonspreading which contains the class of generalized nonspreading mappings in a Banach space and then prove an attractive point theorem for such mappings in a Banach space. Furthermore, we prove a mean convergence theorem of Baillon’s type and a weak convergence theorem of Mann’s type for such nonlinear mappings in a Banach space. These results generalize attractive point, mean convergence and weak convergence theorems proved by Lin and Takahashi [26], and Kocourek, Takahashi and Yao [21] in a Banach space.