In this paper, equation (1) is solved by a nonstationary iterative procedure (2) in a partially ordered Banach space $B$. It is supposed that a positive eigenvalue and corresponding eigenelement of operator $T$ are known. After setting the necessary conditions for series (2), an invariant itnerval (4) for the operator $T'$ is obtained. This made it possible to get an a \emph{posteriori} error estimation. In this way the results (1) are transferred into a non stationary iterative procedure of the type (2).