Convergence results of nonlinear problems based on Tikhonov regularization method

Abstract

In this paper, we study the convergent results of Tikhonov regularization method for solving nonlinear ill-posed problems with noisy operator in Banach spaces. And we give the convergent rates while both the right-hand side of the equation and the operator are given approximately errors. Furthermore we prove that the convergent rates depend on the interplay of the solution smoothness and the nonlinearity structure, and obtain concisely variational inequalities results about them.