R. Khalil

Interpolated Young and Heinz inequalities

In this article, we interpolate the well-known Young’s inequality for numbers and matrices, when equipped with the Hilbert–Schmidt norm, then present the corresponding interpolations of recent refinements in the literature. As an application of these interpolated versions, we study the monotonicity these interpolations obey.

Operator-norm inequalities and interpolated trace inequalities

In this article, we investigate some operator-norm inequalities related to some conjectures posed by Hayajneh and Kittaneh that are related to questions of Bourin regarding a special type of inequalities referred to as subadditivity inequalities. While some inequalities are meant to answer these conjectures, other inequalities present reverse-type inequalities for these conjectures. Then, we present some new trace inequalities related to Heinz means inequality and use these inequalities to prove some variants of the aforementioned conjectures.