Approximation of solutions of nonlinear equations of Hammerstein type in Hilbert space

Authors:
C. E. Chidume and H. Zegeye

Journal:
Proc. Amer. Math. Soc. **133** (2005), 851-858

MSC (2000):
Primary 47H06, 47H15, 47H17, 47J25

Published electronically:
September 29, 2004

MathSciNet review:
2113936

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a real Hilbert space. Let , be bounded monotone mappings with , where and are closed convex subsets of satisfying certain conditions. Suppose the equation has a solution in . Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on , and the operators and need not be defined on compact subsets of .

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Additional Information

**C. E. Chidume**

Affiliation:
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Email:
chidume@ictp.trieste.it

**H. Zegeye**

Affiliation:
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Email:
habz@ictp.trieste.it

DOI:
http://dx.doi.org/10.1090/S0002-9939-04-07568-9

Keywords:
Hilbert spaces,
maximal monotone mappings,
monotone mappings,
range condition

Received by editor(s):
October 8, 2003

Received by editor(s) in revised form:
November 20, 2003

Published electronically:
September 29, 2004

Additional Notes:
The second author undertook this work when he was visiting the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, as a postdoctoral fellow.

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.