IJPAM: Volume 81, No. 1 (2012)
HAMMERSTEIN TYPE OPERATOR EQUATIONS
WITH MONOTONE OPERATORS
Department of Mathematical and Computational Sciences
National Institute of Technology Karnataka
Surathkal, 575 025, INDIA
Abstract. The problem of approximately solving an ill-posed Hammerstein type operator equation in a Hilbert space is considered, where is a bounded linear operator and is a non-linear monotone operator.
The method involves the Dynamical System Method (DSM) - both continuous and iterative schemes, studied by Ramm (2005), and known as Tikhonov regularization. By choosing the regularization parameter according to an adaptive scheme considered by Pereverzev and Schock (2005) an order optimal error estimate has been obtained.
Received: July 27, 2012
AMS Subject Classification: 47H05, 47A52, 65F22, 65J20, 70G60
Key Words and Phrases: ill-posed Hammerstein type operator, dynamical system method, monotone operator, adaptive scheme, Tikhonov regularization
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395