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Funkcije, ki ohranjajo konvergenco vrst : magistrsko delo : na študijskem programu 2. stopnje Matematika = Functions that preserve the convergence of a series
Tetičkovič, Tine
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.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Maribor : [T. Tetičkovič], 2022
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