【摘要】 设E是具弱序列连续对偶映像自反Banach空间, C是E中闭凸集, T:C→ C是具非空不动点集F（T）的非扩张映像.给定u∈ C,对任意初值x0∈ C,实数列{αn}n∞=0,{βn}∞n=0∈ （0,1）,满足如下条件:（i）sum from n=α to ∞α_n=∞, α_n→0;（ii）β_n∈[0,α) for some α∈（0,1）;（iii）sun for n=α to ∞|α_n-1+α_n|<∞,sum from n=α|β_n-1-β_n|<∞设{x_n}_n1^∞是由下式定义的迭代序列:{y_n=β_nx_n+（1-β_n）Tx_n x_n+1=α_nu+（1-α_n）y_n Then {x_n}_n=1^∞则{x_n}_n=1^∞强收敛于T的某不动点.更多还原

【Abstract】 Assume E is a reflexive Banach space which has a weakly continuous duality map,C is a closed convex subset of E and let T:C→C be a nonexpansive mapping such that F（T）≠φ.Given a point u∈C,the initial guess x0∈C is chosen arbitrarily and given sequences {αn}∞n=0,{βn}∞n=0 in（0,1）,the following conditions are satisfied（i）sum from n=α to ∞ α_n=∞, α_n→0;（ii）β_n∈[0,α) for some α∈（0,1）;（iii）sun for n=α to ∞|α_n-1+α_n|<∞,sum from n=α|β_n-1-β_n|<∞ Let {x_n}_n1^∞ be composite process defined by{y_n=β_nx_n+（1-β_n）Tx_n x_n+1=α_nu+（1-α_n）y_n Then {x_n}_n=1^∞ converges strongly to a fixed point of T.更多还原