无限簇非扩张非自映象公共不动点的黏性逼近法

Abstract

Abstract:

Let E be a real strictly convex and reflexive Banach space with a uniformly Gâteaux differentiable norm and K be a nonempty closed convex subset of E which is also a sunny nonexpansive retract of E. Let f : K→K be a contractive mapping, P be a sunny nonexpansive retraction of $E$ onto K and {T_n}_n=1^∞: K→E be a family of countable infinite nonexpansive nonself-mappings such that the common fixed point set F:=:=∩^∞_n=1F(T_n)≠Φ and {λ_n} be a seqence of nonnegative numbers in [0,1]. Consider the following
iterative sequence
              { x_n+1=(1-α_n-β_n)x_n+α_n f(y_n)+β_nW_ny_n,
                 y_n=(1-γ_n-δ_n)x_n+γ_nW_nx_n+δ_nu_n, n ≥1.

where W_n is the W-mapping generated by P, T_n, T_n_-1,  …, T₁and λ_n, λ_n_-1, …, λ₁for n ≥ 1. It is shown that under very mild conditions on the parameters, the sequence {x_n} converges strongly to p ∈ F, where p is the unique solution in F to the following variational inequality
               <(I-f)p, j(p-x*)>≤ 0, ∨_x* ∈ F.

Key words: Nonexpansive nonself-mapping, Uniformly Gâteaux differentiable norm, Viscosity approximation, Common fixed point

CLC Number:

47H10

ZHAO Liang-Cai, ZHANG Shi-Sheng. Viscosity Approximation Methods for Common Fixed Points of Infinite Nonexpansive Nonself-mappings[J].Acta mathematica scientia,Series A, 2010, 30(4): 1144-1157.

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Viscosity Approximation Methods for Common Fixed Points of Infinite Nonexpansive Nonself-mappings

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