Eneström-Kakeyin teorem

master's thesis

• Title (english): Eneström-Kakeyin theorem
• Author: Marija Katarina
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-07-21, 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: Eneström-Kakeyin teorem; nultočke polinoma; rastući niz
• Keywords (english): Eneström-Kakeya theorem; zeros of a polynomial; increasing coeffcients
• Language: croatian
• URN:NBN: urn:nbn:hr:217:654751
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-09-15 10:38:08