Erappa, S.M.George, S.2026-02-052021IAENG International Journal of Applied Mathematics, 2021, 51, 1, pp. -19929978https://idr.nitk.ac.in/handle/123456789/23472An iterative scheme which is free of derivative is employed to approximately solve nonlinear ill-posed Hammer-stein type operator equations )TG(x) = Y, where G is a non-linear monotone operator and ) is a bounded linear operator defined on Hilbert spaces X,Y,Z. 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 U. Furthermore, order optimal error bounds are obtained and the method is validated by a numerical example. © 2021, IAENG International Journal of Applied Mathematics. All Rights Reserved.Convergence of numerical methodsError analysisIterative methodsMathematical operatorsBounded linear operatorsConvergence analysisIterative schemesLipschitz conditionsMonotone operatorsOperator equationOptimal error boundRegularization parametersNonlinear equations