Geodesic
Existence of best approximation elements in the spaces $L_{\varphi_+\varphi_-}$
Contemporary Mathematics and Its Applications, Tome 96 (2015), pp. 112-131.

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In this paper, we examine the problem on the existence of best approximation elements in functional spaces with nonsymmetric norms and sign-sensitive weights. 
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     author = {B. V. Simonov and V. A. Ivanyuk and I. E. Simonova},
     title = {Existence of best approximation elements in the spaces $L_{\varphi_+\varphi_-}$},
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B. V. Simonov; V. A. Ivanyuk; I. E. Simonova. Existence of best approximation elements in the spaces $L_{\varphi_+\varphi_-}$. Contemporary Mathematics and Its Applications, Tome 96 (2015), pp. 112-131. http://geodesic.mathdoc.fr/item/CMA_2015_96_a7/