Young-type inequalities and their matrix analogues

@article{Alzer2015YoungtypeIA,
title={Young-type inequalities and their matrix analogues},
author={H. Alzer and Carlos M. da Fonseca and A. Kova{\vc}ec},
journal={Linear and Multilinear Algebra},
year={2015},
volume={63},
pages={622 - 635}
}

We present several new Young-type inequalities for positive real numbers and we apply our results to obtain the matrix analogues. Among others, for real numbers , and , with and , we prove the inequalitieswhere and are, respectively, the (weighted) arithmetic and geometric means of the positive real numbers and with . In addition, we show that both bounds are sharp. An example of a matrix analogue for the case is the double-inequalityfor positive definite matrices . Our results extend some… CONTINUE READING