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In this article, we study the further refinements and reverses of the Young and Heinz inequalities with the Kantorovich constant. These modified inequalities are used to establish corresponding operator inequalities on Hilbert space and Hilbert-Schmidt norm inequalities., Comment: 11 pages

This note aims to present some reverse inequalities about the power means and Karcher mean via the Kantorovich constant and some of these have been generalized to higher power. Also, we generalize the reverse weighted arithmetic-geometric mean inequality of n positive invertible operators due to Lawson and Lim. In addition, we make comparisons between the Karcher mean and Lawson-Lim geometric mean for higher power., Comment: 18 pages

Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established., Comment: 12 pages

In this paper, we improve and generalize the operator versions of Kantorovich and Wielandt inequalities for positive linear maps on Hilbert space. Our results are more extensive and precise than many previous results due to Fu and He [Linear Multilinear Algebra, doi: 10. 1080/03081087. 2014. 880432.] and Zhang [Banach J. Math. Anal., 9 (2015), no. 1, 166-172.]., Comment: 11 pages