Some quantum $f$-divergence inequalities for convex functions of self-adjoint operators

Ali Taghavi; Vahid Darvish; Haji Mohammad Nazari; Silvestry Sever Dragomir

doi:10.5269/bspm.v37i1.31452

Some quantum $f$-divergence inequalities for convex functions of self-adjoint operators

Ali Taghavi University of Mazandaran Faculty of Mathematical Sciences Department of Mathematics http://orcid.org/0000-0001-6230-733X
Vahid Darvish University of Mazandaran Faculty of Mathematical Sciences Department of Mathematics
Haji Mohammad Nazari University of Mazandaran Faculty of Mathematical Sciences Department of Mathematics
Silvestry Sever Dragomir Victoria University Mathematics, School of Engineering and Science http://orcid.org/0000-0003-2902-6805

DOI: https://doi.org/10.5269/bspm.v37i1.31452

Keywords: Self-adjoint bounded linear operator, Trace inequality, Convex function, Quantum $f$-divergence

Abstract

In this paper, some new inequalities for convex functions of self-adjoint operators are obtained. As applications, we present some inequalities for quantum $f$-divergence of trace class operators in Hilbert Spaces.