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Iterative solutions of parameter-dependent nonlinear equations of hammerstein type

✍ Scribed by M.A. Amer

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
407 KB
Volume
34
Category
Article
ISSN
0898-1221

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✦ Synopsis

The unique solution of a general nonlinear Hammerstein-type equation is obtained based on the contraction mapping principle. Introducing a suitable weighted norm, the range of values of the involved parameter allowed by the contraction mapping principle is shown to be increased. Detailed construction of the suitable weight function is given. Application to a specific Hammerstein integral equation is considered supported by a numerical example.

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hbstract--Iterative solutions of a general nonlinear operator equation of the form Ax + )~Tx = f, where A and T are in general nonlinear operators in an appropriate space, have not been developed so far. In this paper, the three well-known Banach, Mann, and Ishikawa iteration processes are used to f