Karamatova neenakost

diplomsko delo

Polona Dovečar (Author), Uroš Milutinović (Mentor)

Abstract

Diplomsko delo obravnava Karamatovo neenakost, ki je pomemben izrek analize za konveksne funkcije, definirane na nekem intervalu I. Ime je dobila po srbskem matematiku Jovanu Karamati, ki spada med pomembne matematike 20. stoletja. Za izpeljavo obravnavane neenakosti sta sprva definirana ključna pojma, to sta majorizacija in povprečje poljubnih pozitivnih padajočih n-teric a in b. V delu so predstavljene sorodne neenakosti, kot so Jensenova neenakost, Cauchyjeva neenakost ter Schurova in Muirheadova neenakost. Ker se podobne neenakosti velikokrat pojavljajo na matematičnih tekmovanjih, so v zadnjem poglavju predstavljeni primeri tekmovalnih nalog, katerih rešitve so povezane z obravnavano diplomsko tematiko.

Keywords

matematika;analiza;konveksne funkcije;majorizacija;povprečje;Karamatova neenakost;Jensenova neenakost;Cauchyjeva neenakost;neenakosti;Schurova neenakost;Muirheadova neenakost;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2012
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[P. Dovečar]
UDC:	51(043.2)
COBISS:	19186184
Views:	1650
Downloads:	96
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	KARAMATA INEQUALITY
Secondary abstract:	Graduation thesis discusses Karamata inequality, which is very important analysis theorem for convex functions defined on an interval I. Karamata inequality got its name from Serbian mathematician Jovan Karamata, one of the significant mathematicians of 20th century. For derivation of the inequality two key terms are defined, majorization and average of positive descending sequences a and b. Similar inequalities like Jensen's inequality, Cauchy's inequality, Shur's inequality, and Muirhead's inequality are also presented within this thesis. Presented similar inequalities are often a subject of mathematical competitions, therefore in the last chapter several examples of competition problems are given, whose solutions are related to the theme of this graduation thesis.
Secondary keywords:	convex function;majorization;average;Karamata inequality;Jensen's inequality;Cauchy's inequality;Schur's inequality;Muirhead's inequality;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 35 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19980