Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups
نویسندگان
چکیده
Throughout this paper, letH be a real Hilbert space with inner product 〈·,·〉 and ‖ · ‖. We use xn⇀ x to indicate that the sequence {xn} converges weakly to x. Similarly, xn → x will symbolize strong convergence. we denote by N and R+ the sets of nonnegative integers and nonnegative real numbers, respectively. let C be a closed convex subset of a Hilbert space H , and Let T : C → C be a nonexpansive mapping (i.e., ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C). We use Fix(T) to denote the set of fixed points of T ; that is, Fix(T)= {x ∈ C : x = Tx}. We know that Fix(T) is nonempty if C is bounded, for more details see [1]. In [2], Shioji and Takahashi introduce in a Hilbert space the implicit iteration
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