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Introduction to Sublinear Analysis

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Abstract

Basing on the notion of compact subdifferentials, we develop a subdifferential calculus of the first and the second orders beyond the Taylor expansion and extremum theory. We introduce and investigate a comprehensive class of subsmooth maps such that the constructed theory is applicable to them. We develop a technique to investigate one-dimensional extremal variational problems with subsmooth Lagrangians (including sufficient conditions). A number of examples are considered.

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Authors and Affiliations

  1. V. I. Vernadskii Tavria National University, Simferopol’, Russia

    I. V. Orlov

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  1. I. V. Orlov
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Correspondence to I. V. Orlov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 53, Proceedings of the Crimean Autumn Mathematical School-Symposium KROMSH-2013, 2014.

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Orlov, I.V. Introduction to Sublinear Analysis. J Math Sci 218, 430–502 (2016). https://doi.org/10.1007/s10958-016-3039-z

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