Original title: Konvexita v normovaných lineárních prostorech a v obecnějších prostorech
Translated title: Convexity in normed linear spaces and more general spaces
Authors: Zaplatílek, Adam ; Pick, Luboš (advisor) ; Nekvinda, Aleš (referee)
Document type: Bachelor's theses
Year: 2018
Language: eng
Abstract: [eng] [cze]
We study questions concerning convexity and the existence of the nearest point for a given set in spaces equipped with either a norm, or with a more gen- eral functional, namely a quasinorm or an α−norm. We characterize convexity in a Hilbert space. We investigate relations between convexity and properties of the distance function. 1 Studujeme otázky týkající se konvexity a existence nejbližšího bodu pro danou množinu v prostorech s normou, případně kvazinormou nebo α-normou. Dokazujeme jistou charakterizaci konvexity v Hilbertově prostoru. Vyšetřujeme vztahy mezi konvexitou a vlastnostmi funkce vzdálenosti od množiny. 1
Keywords: alternation theorem; element of best approximation; Haar condition; metric space; normed linear space; alternační věta; Haarova podmínka; metrický prostor; normovaný lineární prostor; prvek nejlepší aproximace

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/99514

Permalink: http://www.nusl.cz/ntk/nusl-383854


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses