Fixed point and nonlinear ergodic theorems for new nonlinear mappings in Hilbert spaces (Nonlinear Analysis and Convex Analysis)
Toshiharu Kawasaki, Wataru Takahashi · Kyoto University Research Information Repository (Kyoto University) · 2013
In this paper we introduce a broad class of nonlinear mappings which contains the class of constractive mappings and the class of generahzed hybrid mappings in a Hilbert space.Then we prove a fixed point theorem for such mappings in a Hilbert space.Furthermore, we prove a nonlinear ergodic theorem of Baillon's type in a Hilbert space.Their results generalize the fixed point theorem and the nonlinear ergodic theorem proved by Kocourek, Takahashi and Yao [10].