## Convergence of the steepest descent method for accretive operators

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- by Claudio H. Morales and Charles E. Chidume PDF
- Proc. Amer. Math. Soc.
**127**(1999), 3677-3683 Request permission

## 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 \[ x_{n+1}=x_n-c_n(Ax_n-z),\qquad n=0,1,2,\dots ,\] converges strongly to the unique solution of the equation $Ax=z$, provided that the sequence $\{c_n\}$ fulfills suitable conditions.## References

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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
- MR Author ID: 232629
- Email: chidume@ictp.trieste.it
- Published electronically: May 11, 1999
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**127**(1999), 3677-3683 - MSC (1991): Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-99-04975-8
- MathSciNet review: 1616629