20.500.12556/DKUM-22921 KARAMATOVA NEENAKOST KARAMATA INEQUALITY 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 tudi 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. 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. konveksne funkcije majorizacija povprečje Karamatova neenakost Jensenova neenakost Cauchyjeva neenakost Schurova neenakost Muirheadova neenakost convex function majorization average Karamata inequality Jensen's inequality Cauchy's inequality Schur's inequality Muirhead's inequality true true false [P. Dovečar] Slovenski jezik Angleški jezik Diplomsko delo 2012-05-09 14:48:13 2012-06-12 14:03:10 2022-04-14 12:12:40 2023-12-29 03:32:29 2012 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 19186184 URN:SI:UM:DK:KVJDPDDQ UNI_Dovecar_Polona_2012.pdf UNI_Dovecar_Polona_2012.pdf 1 BD95F52A2A56FD41AA8A3D03DA7B612C 38dc6dff9c9c967091ad67b2d807142d60864432a1c9a25cd075d0ec66865fb8 9ae24514-7c06-11eb-bb7a-00155d0001ca 20.500.12556/dkum/ed69bf4b-cde4-4030-8b13-ba313c2b473b https://dk.um.si/Dokument.php?lang=slv&id=29858 Fakulteta za naravoslovje in matematiko 0 0 0