中文摘要：

主要研究求解增生算子零点问题的一类算法：xn＋1=αnu＋（1-αn）（（1-λ）xn＋λJrnxn）,其u是固定向量, λ∈（0,1）,{rn｝和{αn｝是实数列, Jrn表示增生算子A的预解式.其中（rn）收敛是保证算法收敛的一个充分条件,该文主要证明了此条件可减弱为limn ｜1-rn＋1/rn｜=0.

英文摘要：

This paper deals with the problem：find x so that 0 ∈ Ax,where A is an accretive operator.One algorithm solving this problem has the following scheme：xn＋1=αnu ＋ （1-αn）（（1-λ）xn ＋ λJrnxn）,where u is a fixed element,λ ∈ （0,1）,{rn} and {αn} are real sequences,and Jrn denotes the resolvent of A.The algorithm is known to converge provided that （rn） is a convergent sequence.In this paper we show that such a condition can be relaxed as limn→∞ ｜1-rn＋1/rn｜ =0.