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- W1053375716 abstract "Let (C) be a convex compact subset of a uniformly convex Banach space. Let ({T_t}_{t geq0}) be a strongly-continuous nonexpansive semigroup on (C). Consider the iterative process defined by the sequence of equations $$x_{k+1} =c_k T_{t_{k+1}}(x_{k+1})+(1-c_k)x_k.$$ We prove that, under certain conditions on ({c_k}) and ({t_k}), the sequence ({x_k}_{n=1}^infty) converges strongly to a common fixed point of the semigroup ({T_t}_{t geq0}). There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property, and also weak convergence results in Banach spaces that are simultaneously uniformly convex and uniformly smooth. In this paper, we do not assume the Opial property or uniform smoothness of the norm." @default.
- W1053375716 created "2016-06-24" @default.
- W1053375716 creator A5000690711 @default.
- W1053375716 date "2014-12-15" @default.
- W1053375716 modified "2023-10-18" @default.
- W1053375716 title "Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces" @default.
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- W1053375716 doi "https://doi.org/10.14708/cm.v54i2.703" @default.
- W1053375716 hasPublicationYear "2014" @default.
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