Erappa, Shobha M and George, Santhosh (2021) Derivative Free Iterative Scheme for Monotone Nonlinear Ill-posed Hammerstein-Type Equations. IAENG International Journal of Applied Mathematics, 51 (1). ISSN 1992-9978

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Abstract

—An iterative scheme which is free of derivative is employed to approximately solve nonlinear ill-posed Hammer�stein type operator equations 푇퐺(푥) = 푦, where 퐺 is a non�linear monotone operator and 푇 is a bounded linear operator defined on Hilbert spaces 푋, 푌, 푍. The convergence analysis adapted in the paper includes weaker Lipschitz condition and adaptive choice of Perverzev and Schock(2005) is employed to choose the regularization parameter 훼. Furthermore, order optimal error bounds are obtained and the method is validated by a numerical example

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