Multistep iterative method for solving linear operator equations in Banach spaces

Multistep iterative method for solving the linear operator equation $Ax=y$ with $B$-symmetric $B$-positive operator acting from a Banach space $X$ to a Banach space $Y$ is considered. The space $X$ is assumed to be $p$-convex and uniformly smooth, whereas $Y$ is an arbitrary Banach space. The case of exact data is considered and the weak and strong (norm) convergences of the iterative process are proved.