Geodesic
Influence of geometric properties of space on the convergence of Cauchy's method in the best-approximation problem
Matematičeskie zametki, Tome 8 (1970) no. 3, pp. 329-338.

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The reciprocity of certain geometrical properties of finite-dimensional Banach space is established. The role of these properties in the construction of best-approximation elements by Cauchy's method is investigated. 
@article{MZM_1970_8_3_a5,
     author = {V. I. Berdyshev},
     title = {Influence of geometric properties of space on the convergence of {Cauchy's} method in the best-approximation problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {329--338},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a5/}
}
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V. I. Berdyshev. Influence of geometric properties of space on the convergence of Cauchy's method in the best-approximation problem. Matematičeskie zametki, Tome 8 (1970) no. 3, pp. 329-338. http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a5/