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Compact Subdifferentials in Banach Cones

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Abstract

We construct, in general terms, the theory of first-order compact subdifferentials for mappings acting in Banach cones. The basic properties of K-subdifferentials up to the mean-value theorem and its nontrivial corollaries are studied. An application to variational functionals with nonsmooth integrand is considered.

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Correspondence to Igor’ V. Orlov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 10, No. 4, pp. 532–558, October–November, 2013.

Translated from Russian by V. V. Kukhtin

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Orlov, I.V., Khalilova, Z.I. Compact Subdifferentials in Banach Cones. J Math Sci 198, 438–456 (2014). https://doi.org/10.1007/s10958-014-1801-7

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