Download
PDF 354.06 KB
master's thesis
69   30
Schur - convex Function
Martina Dorić (2017)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group
Cite this document

Dorić, M. (2017). Schur - konveksne funkcije (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:731051

Dorić, Martina. "Schur - konveksne funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:731051

Dorić, Martina. "Schur - konveksne funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:731051

Dorić, M. (2017). 'Schur - konveksne funkcije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 November 2019, https://urn.nsk.hr/urn:nbn:hr:126:731051

Dorić M. Schur - konveksne funkcije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2019 November 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:731051

M. Dorić, "Schur - konveksne funkcije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:731051

Metadata
TitleSchur - konveksne funkcije
Title (english)Schur - convex Function
AuthorMartina Dorić
MentorMihaela Ribičić Penava (mentor)
Committee memberDomagoj Ševerdija (predsjednik povjerenstva)
Committee memberMihaela Ribičić Penava (član povjerenstva)
Committee memberLjerka Jukić Matić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Probability and Mathematical Statistics Research Group)
Osijek
Defense date and country2017-10-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
Cilj ovog rada je sistematizirati neke rezultate o Schur-konveksnim funkcijama koji omogućuju njihovu identifikaciju te ukazati na njihovu ulogu u izvođenju nejednakosti. Prvo se definira majorizacija i navedena su dva motivacijska ekonomska primjera. To su Lorenzova krivulja koja omogućuje grafičku vizualizaciju pojma majorizacije i Daltonovi transferi koji služe kao motivacija definicije T-transformacija. Umnožak T-transformacija je dvostruko-stohastička matrica, a dvostruko stohastičkim matricama se može karakterizirati majorizacija. Schurkonveksne funkcije su funkcije koje čuvaju uredaj majorizacije. Simetričnost koja je važno svojstvo Schur-konveksnih funkcija proizlazi iz činjenice da je svaki vektor majoriziran sa svakom svojom permutacijom. Navedene su tvrdnje koje omogućavaju karakterizaciju i identifi- kaciju Schur-konveksnih funkcija, od kojih su najznačajnije karakterizacije diferencijabilnih Schur-konveksnih funkcija. Navedene su veze Schur-konveksnih funkcija s nekim klasama funkcija poput konveksnih i kvazikonveksnih funkcija te neki primjeri. Schur-konveksne funkcije se primjenjuju u mnogim područjima matematike, od kojih je navedeno nekoliko primjera iz geometrije trokuta i matrične teorije.
Abstract (english)
The purpose of this paper is to systematize some results on Schur convex functions that enable their identification and to point out their role in deriving inequalities. Firstly majorization is defined and two economics examples are given as motivation. Those are Lorenz curve that allows graphical visualisation of majorization and Dalton transfers that are used as motivation for definition of T-transforms. Products of T-transforms are doubly stohastic matrices and doubly stohastic matrices are used to characterize majorization. Schur-convex functions are functions that preserve the ordering of majorization. Symmetry is an important property of Schur-convex functions that arises from the fact that every vector is majorized by its permutations. Results are given that allow characterizations and identifi- cation of Schur-convex functions, where most relevant are characterizations of diferentiable Schur-convex functions. Schur-convex functions are linked to convex and quasi-convex functions and examples are given. Schur-convex functions have many mathematical applications, such as in geometry of triangles and matrix theory.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:731051
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2017-10-25 05:57:05