Geodesic
Multistep iterative method for solving linear operator equations in Banach spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 318-328

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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. 
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     author = {P. A. Chistyakov},
     title = {Multistep iterative method for solving linear operator equations in {Banach} spaces},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {318--328},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_1_a25/}
}
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P. A. Chistyakov. Multistep iterative method for solving linear operator equations in Banach spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 318-328. http://geodesic.mathdoc.fr/item/TIMM_2012_18_1_a25/