Fixed point iteration processes for asymptotically nonexpansive mappings

Proceedings of the American Mathematical Society - Tập 122 Số 3 - Trang 733-739
Kok-Keong Tan, Hong–Kun Xu1,2
1Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa
2Institute of Applied Mathematics, East China University of Science and Technology, Shanghai 200237, China

Tóm tắt

Let X be a uniformly convex Banach space which satisfies Opial’s condition or has a Fréchet differentiable norm, C a bounded closed convex subset of X, and T : C → C T:C \to C an asymptotically nonexpansive mapping. It is then shown that the modified Mann and Ishikawa iteration processes defined by x n + 1 = t n T n x n + ( 1 − t n ) x n {x_{n + 1}} = {t_n}{T^n}{x_n} + (1 - {t_n}){x_n} and x n + 1 = t n T n ( s n T n x n + ( 1 − s n ) x n ) + ( 1 − t n ) x n {x_{n + 1}} = {t_n}{T^n}({s_n}{T^n}{x_n} + (1 - {s_n}){x_n}) + (1 - {t_n}){x_n} , respectively, converge weakly to a fixed point of T.

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Tài liệu tham khảo

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Thông tin xuất bản

Proceedings of the American Mathematical Society

Tập 122 Số 3

733-739

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