Cilj ovog završnog rada je dati pregled nekih diskretnih nejednakosti za realne i kompleksne brojeve. To uključuje nejednakosti između osnovnih sredina, Cauchyevu nejednakost i neka njezina poopćenja i profinjenja, Hölderovu nejednakost te nejednakost Minkowskog. Nadalje, rad obuhvaća Abelovu i Čebiševljevu nejednakost te Grüssovu i Biernacki nejednakost. Na kraju, donosi kratki pregled nejednakosti za konveksne funkcije kao što su Jensenova i Petrovićeva nejednakost.

The main purpose of this paper is to provide an overview of some discrete inequalities for real and complex numbers. These include: inequalities between elementary means, the Cauchy inequality as well as some refinements and generalisations of Cauchy inequality. Furthermore, the paper encompasses the Abel inequality, Čebyšev’s inequality,the Grüss inequality and the Biernacki inequality. Lastly, it brings brief survey of inequalities for convex functions such as Jensen’s inequality and the Petrović inequality.