prikaz prve stranice dokumenta Eneström-Kakeyin teorem
  Download
PDF 371.84 KB
master's thesis
Eneström-Kakeyin teorem
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:654751
Katarina, Marija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Katarina, M. (2021). Eneström-Kakeyin teorem (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:654751

Katarina, Marija. "Eneström-Kakeyin teorem." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:654751

Katarina, Marija. "Eneström-Kakeyin teorem." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:654751

Katarina, M. (2021). 'Eneström-Kakeyin teorem', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:654751

Katarina M. Eneström-Kakeyin teorem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:654751

M. Katarina, "Eneström-Kakeyin teorem", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:654751

Metadata
TitleEneström-Kakeyin teorem
Title (english)Eneström-Kakeyin theorem
AuthorMarija Katarina
MentorSanja Varošanec (mentor)
Committee memberSanja Varošanec (predsjednik povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
Committee memberRudi Mrazović (član povjerenstva)
Committee memberGoran Radunović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-07-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Tema ovog diplomskog rada je Eneström-Kakeyin teorem, jedan od osnovnih teorema koji opisuje položaj nultočaka polinoma, i njegove generalizacije. Najprije je iskazan i dokazan sam Eneström-Kakeyin teorem, a potom je dan kratki povijesni osvrt o njegovom nastanku. U spomenutom se teoremu promatraju polinomi s realnim koeficijentima koji su nenegativni i čine rastući niz. Promjenama pretpostavki teorema ili promatranjem posebnih slučajeva drugih teorema vezanih za položaj nultočaka polinoma dolazi se do generalizacija i profinjenja Eneström-Kakeyinog teorema. Pri tome je napravljena podjela na polinome čiji koeficijenti čine rastući niz i na polinome čiji koeficijenti čine niz koji je do nekog člana rastući, a zatim pada.
Abstract (english)
The topic of this thesis is the Eneström-Kakeya theorem, one of the basic theorems that describes the position of zeros of a polynomial, and its generalizations. The Eneström-Kakeya theorem is stated and proved in the second chapter. Also, a brief historical overview of its origin is given. In the mentioned theorem, we observe polynomials with real nonnegative monotone increasing coeffcients. Generalizations and refinements of the Eneström- Kakeya theorem are made by changing the assumptions of the theorems or observing special cases of other theorems related to the position of the zeros of a polynomial. Our results are divided into two groups. The first group includes results about polynomials whose coeffcients form an increasing sequence, while the second group includes results about polynomials whose coeffcients form a sequence that is increasing until a certain member and then it is decreasing.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:654751
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-09-15 10:38:08