Geodesic
$\theta$-metric function
Izvestiya. Mathematics , Tome 88 (2024) no. 2, pp. 369-388

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We study approximative properties of sets as a function of the rate of variation of the distance function defined in terms of some continuous functional (in lieu of a metric). As an application, we prove non-uniqueness of approximation by non-convex subsets of Hilbert spaces with respect to special continuous functionals. Results of this kind are capable of proving non-uniqueness solvability for gradient-type equations.
Keywords: asymmetric space, $\theta$-metric function, minimization of functionals, differential equation, $\theta$-metric projection.
Mots-clés : non-unique solvability 
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     author = {I. G. Tsar'kov},
     title = {$\theta$-metric function},
     journal = {Izvestiya. Mathematics },
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I. G. Tsar'kov. $\theta$-metric function. Izvestiya. Mathematics , Tome 88 (2024) no. 2, pp. 369-388. http://geodesic.mathdoc.fr/item/IM2_2024_88_2_a8/