ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 47H05, 47H06, 47H15, 47H17 Osilike, Micah Okwuchukwu, Department of Mathematics, University of Nigeria, Nsukka, Nigeria Iterative solutions of nonlinear equations of the accretive type Suppose E is a real uniformly smooth Banach space and T : E → E is a demicontinuous ∅-strongly accretive operator. Strong convergence theorems for the iterative approximation of the solution of the equation T χ = f , f ∈ E are proved using both the Mann and Ishikawa iteration methods. A related result deals with the iterative approximation of fixed points of ∅-hemicontractive operators—a class of operators more general than the important class of strong pseudocontractions.