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EQUILIBRIUM POINTS FOR A SYSTEM INVOLVING M-ACCRETIVE OPERATORS

Published online by Cambridge University Press:  20 January 2009

C. E. Chidume  and
M. O. Osilike
C. E. Chidume
Affiliation:
The Abdus Salam International Centre for Theoretical Physics, PO Box 586, 34100 Trieste, IT
M. O. Osilike
Affiliation:
Department of Mathematics, University of Nigeria, Nsukka, NG
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Abstract

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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

Keywords

uniformly smooth spacesaccretive operatorspseudocontractive operatorsIshikawa and Mann iterative methodsfixed pointsequilibrium points
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 187 - 199
Copyright
Copyright © Edinburgh Mathematical Society 2001