Strong Convergence Theorems for Asymptotically Nonexpansive Nonself- Mappings
نویسندگان
چکیده
Suppose C is a nonempty bounded closed convex retract of a real uniformly convex Banach space X with uniformly Gâteaux differentiable norm and P as a nonexpansive retraction of X onto C. Let T : C −→ X be an asymptotically nonexpansive nonself-map with sequence {kn}n≥1 ⊂ [1,∞), lim kn = 1, F (T ) = {x ∈ C : Tx = x}, and let u ∈ C. In this paper we study the convergence of the sequences {xn} and {yn} which defined by xn = ( 1− tn kn ) u + tn kn (PT )xn and yn = P (( 1− tn kn ) u + tn kn T (PT )n−1yn ) , where tn = min { 1− (kn − 1) 2 , 1− 1 n } for n = 1, 2, . . ..
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