On the achievable level of accuracy in solving abstract ill-posed problems and nonlinear operator equations in Banach space

It is shown that for a wide class of ill-posed problems of finding the value of a discontinuous operator on an approximate element in Banach space, the level of accuracy of the resulting solution cannot exceed in order the error level of the input data. A similar result is established for a class of nonlinear operator equations with an approximate right-hand side. The classes of problems for which these orders coincide are specified.