On the Convergence of Iteration Processes for Semigroups of Nonlinear Mappings in Banach Spaces
نویسندگان
چکیده
Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the convergence of the generalized Krasnosel’skiiMann and Ishikawa iteration processes to common fixed points of pointwise Lipschitzian semigroups of nonlinear mappings Tt : C → C. Each of Tt is assumed to be pointwise Lipschitzian, that is, there exists a family of functions αt : C → [0,∞) such that ‖Tt(x)− Tt(y)‖ ≤ αt(x)‖x− y‖ for x, y ∈ C. MSC: Primary 47H09; Secondary 47H10.
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