Funkcije, ki ohranjajo konvergenco vrst

magistrsko delo

Tine Tetičkovič (Author), Iztok Banič (Mentor)

Abstract

V magistrskem delu vpeljemo funkcije, ki ohranjajo konvergenco vrst. To so funkcije \newline ▫$f:\RR \longrightarrow \RR$▫, za katere velja, da iz konvergence vrste ▫$\sum\limits_{n = 1}^{\infty}a_n$▫ sledi konvergenca vrste ▫$\sum\limits_{n = 1}^{\infty}f(a_n)$▫. Glavni cilj magistrskega dela je podati in dokazati enostavno karakterizacijo takih funkcij. Najprej bomo predstavili osnovne pojme iz Analize in Algebre, ki so potrebni za razumevanje rezultatov, ki jih opisujemo v magistrskem delu. V drugem poglavju podamo in dokažemo glavni izrek magistrskega dela o karakterizaciji funkcij, ki ohranjajo konvergenco vrst. V zadnjem poglavju preučujemo posplošitve takih funkcij. Natančneje, definiramo lastnost, kot so biti ▫$(c, ac)$▫, ▫$(ac,c)$▫, ▫$(acp)$▫ funkcija, in dokažemo zanimive rezultate za opisane razrede funkcij.

Keywords

magistrska dela;algebra;absolutna vrednost;funkcija;konvergentnost;limita;vrsta;vektorski prostor;zaporedje;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[T. Tetičkovič]
UDC:	512.5(043.2)
COBISS:	105793539
Views:	206
Downloads:	58
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Functions that preserve the convergence of a series
Secondary abstract:	This Master’s thesis introduces a family of function that preserve the convergence properties of a series. Namely these are functions ▫$f:\RR \longrightarrow \RR$▫: such that if ▫$\sum\limits_{n = 1}^{\infty}a_n$▫ converges then ▫$\sum\limits_{n = 1}^{\infty}f(a_n)$▫ also converges. The main aim of the thesis is to mathematically determine a simple characterisation of such functions. First, some background from Analysis and Algebra is introduced. The second chapter provides and proves the main theorem that characterises functions that preserve the convergence of a series. The final chapter investigates a generalisation of such functions. Specifically, some special kinds of functions are defined, such as ▫$(c, ac)$▫, ▫$(ac,c)$▫, ▫$(acp)$▫ functions, which leads to interesting results for these classes of functions.
Secondary keywords:	master theses;algebra;absolute value;function;convergence;limit;series;vector space;sequence;Algebra;Vektorski prostori;Univerzitetna in visokošolska dela;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	VIII, 43 f.
ID:	14368955