Geodesic
Iterative methods for solving linear operator equations in Banach spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 303-318

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Iterative methods for solving the linear operator equation $Ax=y$ with $B$-symmetric $B$-positive operator acting from a Banach space $X$ to a Banach space $Y$ are considered. The space $X$ is assumed to be uniformly convex and smooth, whereas $Y$ is an arbitrary Banach space. The cases of exact and disturbed data are considered and the strong (norm) convergence of the iterative processes is proved.
Keywords: iterative method, duality mapping, $B$-symmetric operator, $B$-positive operator, Bregman distance, uniformly convex space, smooth space, Xu–Roach characteristic inequality, modulus of smoothness of a space.
Mots-clés : minimum-norm solution 
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     author = {P. A. Chistyakov},
     title = {Iterative methods for solving linear operator equations in {Banach} spaces},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {303--318},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a30/}
}
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P. A. Chistyakov. Iterative methods for solving linear operator equations in Banach spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 303-318. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a30/