Approximating Fixed Points of Non-self Asymptotically Nonexpansive Mappings in Banach Spaces
نویسندگان
چکیده
Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be an asymptotically nonexpansive mapping with {kn} ⊂ [1,∞) such that ∑∞ n=1(kn − 1) <∞ and F(T) is nonempty, where F(T) denotes the fixed points set of T . Let {αn}, {α′n}, and {α′′ n } be real sequences in (0,1) and ≤ αn,α′n,α′′ n ≤ 1− for all n ∈N and some > 0. Starting from arbitrary x1 ∈ K , define the sequence {xn} by x1 ∈ K , zn = P(α′′ n T(PT)xn + (1− α′′ n )xn), yn = P(α′nT(PT)zn + (1−α′n)xn), xn+1 = P(αnT(PT)yn + (1−αn)xn). (i) If the dual E∗ of E has the Kadec-Klee property, then {xn} converges weakly to a fixed point p ∈ F(T); (ii) if T satisfies condition (A), then {xn} converges strongly to a fixed point p ∈ F(T).
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