Generalized Extreme Elements

D. A. Klyushin (), S. I. Lyashko (), D. A. Nomirovskii (), Yu. I. Petunin () and V. V. Semenov ()
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D. A. Klyushin: Kyiv National Taras Shevchenko University
S. I. Lyashko: Kyiv National Taras Shevchenko University
D. A. Nomirovskii: Kyiv National Taras Shevchenko University
Yu. I. Petunin: Kyiv National Taras Shevchenko University
V. V. Semenov: Kyiv National Taras Shevchenko University

Chapter Chapter 8 in Generalized Solutions of Operator Equations and Extreme Elements, 2012, pp 163-194 from Springer

Abstract: Abstract Chapter is devoted to the concept of generalized solution of extreme problems. In Sect. 8.1 we give necessary motivations and the definition of generalized extreme element of bounded continuous functional defined of a bounded closed subset of a Banach space. In Sect. 8.2 we prove the theorem on existence of the generalized extreme element of a linear continuous functional. In Sect. 8.3 we study an interest issue concerning the possibility of compact dense embedding of linear normed space in Banach one. The purpose of Sects. 8.4 and 8.5 is to develop the theory of generalized solvability of convex minimization problems in infinite-dimensional Banach spaces.

Keywords: Banach Space; Unit Ball; Extreme Problem; Linear Normed Space; Separable Banach Space (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0619-8_8

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