Convergence of the steepest descent method for accretive operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Convergence of the steepest descent method for accretive operators

Authors:	Claudio H Morales Charles E Chidume

Institution:	Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899 ; International Centre for Theoretical Physics, P. O. Box 586, 34100, Trieste, Italy

Abstract:	Let be a uniformly smooth Banach space and let $A\colon X\to X$ be a bounded demicontinuous mapping, which is also $\alpha$ -strongly accretive on . Let $z\in X$ and let be an arbitrary initial value in . Then the approximating scheme $\begin{displaymath}x_{n+1}=x_n-c_n(Ax_n-z),\qquad n=0,1,2,\dots,\end{displaymath}$ converges strongly to the unique solution of the equation , provided that the sequence $\{c_n\}$ fulfills suitable conditions.

Keywords:	Uniformly smooth space $\alpha$-strongly accretive

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