Local and global H\"older- and Minkowski-type inequalities for nonsymmetric generalized Bajraktarevi\'c means

TL;DR

This paper explores generalized inequalities similar to Minkowski and H"older, using Bajraktarević means and generalized operations, and introduces concepts of local and global validity for these inequalities.

Contribution

It introduces the concepts of local and global validity of generalized inequalities involving Bajraktarević means and characterizes these inequalities in both contexts.

Findings

Characterization of local and global inequalities

Extension of classical inequalities to generalized means

Framework for analyzing inequalities with generalized operations

Abstract

The aim of this paper is to investigate inequalities that are analogous to the Minkowski and H\"older inequalities by replacing the addition and the multiplication by a more general operation, and instead of using power means, generalized Bajraktarevi\'c 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.