Banach空间中关于增生算子的强收敛迭代序列

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Abstract:

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: x_n₊₁=α_nu+(1-α_n)((1-λ)x_n+λJr_nx_n), where u is a fixed element, λ(0,1), {r_n} and α_n are real sequences, and Jr_n denotes the resolvent of A. The algorithm is known to converge provided that (r_n) is a convergent sequence. In this paper we show that such a condition can be relaxed as lim_n→∞|11-r_n+1/r_n|=0.

Key words: Accretive operator, Resolvent, Weakly continuous duality map

CLC Number:

47H06

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CUI Huan-Huan. An Iterative Sequence with Norm Convergence for Accretive Operators in Banach Spaces[J].Acta mathematica scientia,Series A, 2014, 34(3): 755-759.

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An Iterative Sequence with Norm Convergence for Accretive Operators in Banach Spaces

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