Lavrentiev regularization of nonlinear ill-posed equations in Banach and Hilbert space

An iterative method for approximating solutions of nonlinear ill-posed equations with m-accretive (in Banach space)/ monotone (in Hilbert space) operator is considered with weaker assumptions. Precisely, Lavrentiev regularization method is studied in Banach space with m-accretive operator and in Hilbert space with monotone operator. An optimal order of convergence is obtained with a new source condition and apriori parameter choice strategy as in S. George et.al., [16]. Numerical example is presented, which justifies the analysis.