Reverses of Young type inequalities

Abstract

Abstract. This paper aims to give reverses of Young type inequalities which were established by Kai [4]. Then we use these inequalities to establish corresponding inequalities for matrices. Also we present a refinement of the trace version of Young's inequality.Mathematics subject classification (2010): 15A45, 15A60.

An Application of Hölder's Inequality to Economics

“…At its core, the following lemma rests on simple geometrical facts. For a proof, see Hardy et al (1952) and for generalizations to convolutions and matrices of reverse Young's inequality (from which the reverse Hölder inequality follows) see Barthe (1998) and Burqan et al (2015), respectively.…”

A new young type inequality involving Heinz mean

“…Afterwards, Burqan and Khandaqji in [2] presented the reverse of (1.9) and (1.10), which can be stated in the following form…”

“…1 2 , arranged in decreasing order and repeated according to multiplicity. Moreover, it is well known that ||.|| 2 is unitarily invariant.…”

Refinements and reverses of Young type inequalities

“…where h = b a , r = min{2v, 1 − 2v} and r = min{2r, 1 − 2r}. Furthermore, authors in [2] proved that…”