The case a non self-conjugated problem with a posteriori choice of parameter regularization for implicit iteration method for solution of the linear equations with approximately operator

The implicit iteration method for solution of the first-kind operator equations with a non self-conjugated bounded operator in the Hilbert space is proposed. Convergence of a method is proved in case of an a posteriori choice of number of iterations in ussual norm of Hilbert space, supposing that not only the right part of the equation but the operator as well have errors. The estimation of an error of method and estimation of a posteriori moment of stop are received.