V magistrskem delu so obravnavane aditivne in konveksne funkcije. Aditivne funkcije so definirane s Cauchyjevo funkcijsko enačbo, konveksne pa s pomočjo Jensenove neenakosti. Za ene in druge se ...izkaže, da so bodisi zvezne bodisi povsod nezvezne. V primeru aditivnih funkcij je dokaz preprostejši kot za konveksne funkcije. V dokazu zveznosti konveksnih funkcij potrebujemo konveksno ogrinjačo, omejenost funkcije, lokalno omejenost funkcije in enakomerno zveznost na racionalni daljici. V delu so navedene funkcijske neenačbe konveksnih funkcij, ki sledijo iz osnovne Jensenove neenakosti. Poudarek je na neenakosti, ki velja za zvezne in konveksne funkcije. Posebej so obravnavane zvezne in konveksne funkcije na odprtem intervalu ter nekatere klasične neenakosti, katere izpeljemo iz lastnosti teh funkcij.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Ljubljana : [A. Brlogar], 2016
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