This dissertation consists of 4 main chapters. In the first one we introduce the definition of the generalized Bajraktarević mean and compute its partial derivatives up to third-order. Then, separated into 3 further chapters, we investigate some important functional equations and inequalities related to the class of means in question. In the second one we deal with the equality problem of n-variable generalized Bajraktarević means. In the third chapter we investigate the local and global comparison of two n-variable generalized Bajraktarević means. The aim of the fourth chapter is to investigate inequalities that are analogous to the Hölder and Minkowski inequalities by replacing the addition and the multiplication by a more general operation, and instead of using power means, generalized Bajraktarević means, and in particular, weighted Gini means, are considered. A further aim is to characterize such inequalities both in the local and in the global sense.