Abstract and Applied Analysis

Iterative approximation of solutions of nonlinear equations of Hammerstein type

C. E. Chidume and H. Zegeye

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Abstract

Suppose X is a real q-uniformly smooth Banach space and F,K:XX with D(K)=F(X)=X are accretive maps. Under various continuity assumptions on F and K such that 0=u+KFu has a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Our method of proof is of independent interest.

Article information

Source
Abstr. Appl. Anal., Volume 2003, Number 6 (2003), 353-365.

Dates
First available in Project Euclid: 15 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050425967

Digital Object Identifier
doi:10.1155/S1085337503209052

Mathematical Reviews number (MathSciNet)
MR1982807

Zentralblatt MATH identifier
1031.47045

Subjects
Primary: 47H06: Accretive operators, dissipative operators, etc. 47H15
Secondary: 47H17 47J25

Citation

Chidume, C. E.; Zegeye, H. Iterative approximation of solutions of nonlinear equations of Hammerstein type. Abstr. Appl. Anal. 2003 (2003), no. 6, 353--365. doi:10.1155/S1085337503209052. https://projecteuclid.org/euclid.aaa/1050425967


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