Abstract and Applied Analysis

Iterative approximation of solutions of nonlinear equations of Hammerstein type

Abstract

Suppose $X$ is a real $q$-uniformly smooth Banach space and $F,K: X\rightarrow X$ 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

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