Ergodic Convergence Theorem for Nonlinear Mappings in Banach Spaces
Qiao Qing-rong · Journal of Huaihai Institute of Technology · 2005
Let X be a Banach space, (X,τ) a local convex linear topological space, C a τ-sequence compact convex subset of X, and T an asymptotically nonexpansive mapping with the property (Γ) from C to itself, we give the ergodic convergence theorem for asymptotically nonexpansive mapping under uniformly τ-opial condition. Result presented in this paper is the first ergodic convergence theorem in Banach space; therefore it further expands recent related results in other researches.