Iterative approximation of solutions of nonlinear equations of Hammerstein type

被引：15

作者：

Chidume, C. E. ^{[1
]}

Djitte, N. ^{[2
]}

机构：

[1] Abdus Salam Int Ctr Theoret Phys, Trieste, Italy

[2] Univ Gaston Berger, St Louis, Senegal

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 11期

关键词：

Accretive operators; q-uniformly smooth spaces; Duality maps; Uniformly continuous multi-valued maps; INTEGRAL-EQUATIONS; BANACH-SPACES; FIXED-POINTS; ACCRETIVE-OPERATORS; MONOTONE OPERATORS; OPEN QUESTIONS; HILBERT-SPACE; EPSILON-X; MAPPINGS; EXISTENCE;

D O I：

10.1016/j.na.2008.08.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Suppose X is a real q-uniformly smooth Banach space and F, K : X -> X are Lipschitz phi-strongly accretive maps with D(K) = F(X) = X. Let u* denote the unique solution of the Hammerstein equation U + KFu = 0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u*. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. (c) 2008 Elsevier Ltd. All rights reserved.

引用

页码：4086 / 4092

页数：7

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