@article {MATHEDUC.06515124,
author = {Ceau\c{s}u, Traian},
title = {About the equivalence of some classical inequalities. I.},
year = {2015},
journal = {Gazeta Matematic\u{a}. Seria B},
volume = {120},
number = {4},
issn = {1584-9333},
pages = {171-179},
publisher = {Romanian Mathematical Society (Societatea de \c{S}tiin\c{t}e Matematice din Rom\^ania), Bucharest},
abstract = {Summary: The equivalence of the classical inequalities studied in [{\it G. H. Hardy} et al., Inequalities. Cambridge: Univ. Press (1934; Zbl 0010.10703); {\it L. Maligranda}, Math. Inequal. Appl. 1, No. 1, 69--83 (1998; Zbl 0889.26001); ibid. 4, No. 2, 203--207 (2001; Zbl 0987.26011); {\it A. W. Marshall} and {\it I. Olkin}, Inequalities: theory of majorization and its applications. New York etc.: Academic Press (1979; Zbl 0437.26007)], follows from Jensen inequality as a property of the convex functions. Following a long way, but simple and generally, in this paper we show that the equivalence of classical inequalities in finite dimensional case can be proved without using directly Jensen inequality.},
msc2010 = {H30xx (I30xx)},
identifier = {2016a.00695},
}