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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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