Multistep iterative method for solving linear operator equations in Banach spaces

P. A. Chistyakov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: 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.

Keywords: iterative method, duality mapping, $B$-symmetric operator, $B$-positive operator, Bregman distance, Bregman projection, uniformly convex space, smooth space, Xu–Roach characteristic inequality, modulus of smoothness of a space.

UDC: 517.983.54+517.988

Received: 30.09.2011

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