Further results on positively homogeneous subadditive functions by using Csiszár f-divergence

In this paper, motivated by Kluza and Niezgoda (Math Inequal Appl 21(2):455–467, 2018) and Marinescu et al. (J Math Inequal 7:151–159, 2013), we prove Sherman type theorems for positively homogeneous subadditive functions of one or two variables using recent results on Csiszár’s f-divergence. In particular, we provide an extension of the Hardy–Littlewood–Pólya–Karamata (HLPK) theorem for such functions by replacing stochastic matrices with entrywise positive ones. As applications, we present results of HLPK type for some classical inequalities (Radon, Milne, Hölder, Minkowski, Tsallis, Hellinger), which develops the methods and theory of Marinescu et al. (2013).