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EQUILIBRIUM POINTS FOR A SYSTEM INVOLVING M-ACCRETIVE OPERATORS
Published online by Cambridge University Press: 20 January 2009
Abstract
Let $E$ be a real uniformly smooth Banach space and let $A$ be a nonlinear $\phi$-strongly quasi-accretive operator with range $R(A)$ and open domain $D(A)$ in $E$. For a given $f\in E$, let $A$ satisfy the evolution system $\rd u(t)/\rd t+Au(t)=f$, $u(0)=u_0$. We establish the strong convergence of the Ishikawa and Mann iterative methods with appropriate error terms recently introduced by Xu to the equilibrium points of this system. Related results deal with the strong convergence of the iterative methods to the fixed points of $\phi$-strong pseudocontractions defined on open subsets of $E$.
AMS 2000 Mathematics subject classification: Primary 47H06; 47H15; 47H17
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 187 - 199
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- Copyright © Edinburgh Mathematical Society 2001
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