Konveksne funkcije

magistrsko delo

Marko Obid (Author), Marko Slapar (Mentor)

Abstract

V prvem delu magistrskega dela je obravnavana konveksnost funkcij ene spremenljivke. Deﬁniciji konveksnosti in osnovnim lastnostim le-te, sledi uvedba pomembnega pojma Jensenove neenakosti. Obravnavana je zveznost in odvedljivost konveksnih funkcij ter dokazana povezava med konveksnostjo in drugim odvodom neke funkcije. Sledi obravnava polkonveksnosti in kvazikonveksnosti, za zaključek prvega dela pa je predstavljena še funkcija Γ v povezavi s konveksnostjo. V drugem delu je obravnavana konveksnost funkcij več spremenljivk, pri čemer je poudarek na povezavi med konveksno množico in konveksno funkcijo ter med lastnostmi obeh. Zadnje poglavje se znova ukvarja z Jensenovo neenakostjo in z izpeljavo drugih neenakosti.

Keywords

konveksnost;konveksna množica;konveksna krivulja;Jensenova neenakost;zveznost;odvod;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.09 - Master's Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[M. Obid]
UDC:	51(043.2)
COBISS:	12192585
Views:	572
Downloads:	131
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Convex functions
Secondary abstract:	In the ﬁrst part of this master’s thesis, a convexity of functions of one variable is discussed. Following the deﬁnition and basic facts of convexity, the concept of Jensen’s inequality is introduced, followed by the continuity and diﬀerentiability of convex functions, where also a connection between the convexity and a second derivative of the function is proved. Then a concept of semi-convexity and quasiconvexity is introduced. The ﬁrst part is concluded by presentation of the Γ function in connection with convexity. In the second part of thesis, the convexity of functions of more variables, or better, the convexity in a ﬁnite dimensional vector space is discussed. The emphasis is on the connection between convex sets and convex functions, where the properties of both are connected. The last section deals again with Jensen’s inequality and the other inequalities, derived from it.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Predmetno poučevanje
Pages:	47 str.
ID:	10985163