The Iterative Approximation of the Fixed Points with Errors for Asymptotically Quasi-nonexpansive Type Mappings in Banach Spaces
Wang Shao-rong · Journal of Sichuan Normal University · 2004
Let D be a nonempty bounded closed convex subset of a real uniformly convex Banach space E, T:D→D be a semi-compact uniformly L-Lipschitzian asymptotically quasi-nonexpansive type mapping, and {x_n}D be an Ishikawa iterative sequence with mixed errors. The purpose of this paper is to study the strong convergence of {x_n} to a fixed point of T without the condition “for any {x_(n_i)}{x_n}, ‖Tx_(n_i)-x_(n_i)‖→0 as ‖T~~~(n_i)___(x_(n_i))-x_(n_i)‖→0,”. The results presented in this paper extend and improve the recent corresponding results.