Local and global Hölder- and Minkowski-type inequalities for nonsymmetric generalized Bajraktarević means

Abstract

The aim of this paper is to investigate inequalities that are analogous to the Minkowski and Hölder inequalities by replacing the addition and the multiplication by a more general operation, and instead of using power means, generalized Bajraktarević means are considered, in particular, Gini means. A further aim is to introduce the concept of local and global validity of such inequalities and to characterize them in both senses.