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 Mat. Sb. (N.S.), 1971, Volume 85(127), Number 3(7), Pages 420–430 (Mi msb3263)

On stability of extremal problems in Banach space

V. F. Sholohovich

Abstract: Problems of stability and a method of regularization of extremal problems in Banach spaces are considered. Criteria for the convergence and stability of the method considered are given in terms of the geometry of the unit balls of the Banach spaces for a wide class of functionals and restrictions. A means of reducing the problems to a finite-dimensional analog is indicated. The connection with known conditions for the convergence of minimizing sequences in extremal problems is discussed.
Bibliography: 19 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:3, 417–427

Bibliographic databases:

UDC: 513.881
MSC: Primary 41A65; Secondary 46B99

Citation: V. F. Sholohovich, “On stability of extremal problems in Banach space”, Mat. Sb. (N.S.), 85(127):3(7) (1971), 420–430; Math. USSR-Sb., 14:3 (1971), 417–427

Citation in format AMSBIB
\Bibitem{Sho71} \by V.~F.~Sholohovich \paper On stability of extremal problems in Banach space \jour Mat. Sb. (N.S.) \yr 1971 \vol 85(127) \issue 3(7) \pages 420--430 \mathnet{http://mi.mathnet.ru/msb3263} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=290227} \zmath{https://zbmath.org/?q=an:0224.49029} \transl \jour Math. USSR-Sb. \yr 1971 \vol 14 \issue 3 \pages 417--427 \crossref{https://doi.org/10.1070/SM1971v014n03ABEH002625}