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Convergence of the steepest descent method for accretive operators

Author(s): Claudio H. Morales; Charles E. Chidume
Journal: Proc. Amer. Math. Soc. 127 (1999), 3677-3683.
MSC (1991): Primary 47H10
Posted: May 11, 1999
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Abstract: Let $X$ 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 $X$. Let $z\in X$ and let $x_0$ be an arbitrary initial value in $X$. 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 $Ax=z$, provided that the sequence $\{c_n\}$ fulfills suitable conditions.

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Additional Information:

Claudio H. Morales
Affiliation: Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899
Email: morales@math.uah.edu

Charles E. Chidume
Affiliation: International Centre for Theoretical Physics, P. O. Box 586, 34100, Trieste, Italy
Email: chidume@ictp.trieste.it

DOI: 10.1090/S0002-9939-99-04975-8
PII: S 0002-9939(99)04975-8
Keywords: Uniformly smooth space, $\alpha$-strongly accretive
Posted: May 11, 1999
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1999, American Mathematical Society

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