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master's thesis
Kvaziaritmetičke sredine
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:729607
Lovrić, Sanja
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Lovrić, S. (2016). Kvaziaritmetičke sredine (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:729607

Lovrić, Sanja. "Kvaziaritmetičke sredine." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:729607

Lovrić, Sanja. "Kvaziaritmetičke sredine." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:729607

Lovrić, S. (2016). 'Kvaziaritmetičke sredine', Master's thesis, University of Zagreb, Faculty of Science, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:729607

Lovrić S. Kvaziaritmetičke sredine [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:217:729607

S. Lovrić, "Kvaziaritmetičke sredine", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:729607

Metadata
TitleKvaziaritmetičke sredine
AuthorSanja Lovrić
MentorZlatko Pavić (mentor)
MentorSanja Varošanec (mentor)
Committee memberZlatko Pavić (predsjednik povjerenstva)
Committee memberSanja Varošanec (član povjerenstva)
Committee memberDragutin Svrtan (član povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-04-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu proučavaju se kvaziaritmetičke sredine. Rad se sastoji od četiriju poglavlja. Prvo poglavlje se bavi pojmom konveksnosti. Dokazana su brojna svojstva konveksnih funkcija te navedeni primjeri istih. Drugo poglavlje izučava diskretni i integralni oblik Jensenove i Hermite-Hadamardove nejednakosti. Navedene nejednakosti korištene su pri uspoređivanju matematičkih sredina. U trećem poglavlju proučavaju se aritmetička, geometrijska i harmonijska sredina i osnovne integralne sredine: aritmetička, identrička i logaritamska. Na kraju poglavlja navedene sredine su poredane po veličini. Četvrto poglavlje se bavi diskretnim i integralnim kvaziaritmetičkim sredinama. Dokazan je osnovni teorem koji govori o poretku kvaziaritmetičkih sredina. Na kraju rada uvedene su potencijske sredine kao poseban slučaj diskretnih i logaritamske sredine kao poseban slučaj integralnih kvaziaritmetičkih sredina.
Abstract (english)
This graduate thesis studies quasiarithmetic means. The paper consists of four chapters. The first chapter deals with the concept of convexity. Numerous properties of convex functions are proven and examples of convex functions are provided. The second chapter studies discrete and integral form of Jensen’s and Hermite-Hadamard’s inequalities. These inequalities are used for comparison of mathematical means. The third chapter examines arithmetic, geometric and harmonic means and basic integral means: arithmetic, identric and logarithmic. At the end of the chapter all aforementioned means are sorted by size. The fourth chapter deals with discrete and integral quasiarithmetic means. The basic theorem which refers to order of quasiarithmetic means is proven. End of the paper introduces power means as a special case of discrete and logarithmic means as a special case of integral quasiarithmetic means.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:729607
Study programmeTitle: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education
Course: Mathematics and Computer Science Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-28 12:06:09