In this paper, for each alpha is an element of [ 0 , 1 ] and two positive semidefinite matrices A and B , we show the monotonicity decreasing property on q of-Tr[A(1-q)T alpha/q - Tr [( A (q) || B- q )] for 0 < alpha < q < q 1, which implies an Ando-Hiai result that complements Hiai-Petz inequality as q down arrow 0, where T (alpha) ( A || B ) = A#B-alpha - A/alpha.

In this paper, we shall obtain several extensions of log-majorization of Gan-Liu-Tam type.

In this paper, firstly, we shall show reverse of Fujii-Seo type log-majorization, and discuss the equivalence between the log-majorization and Furuta inequality with negative power. At last, we show its application to the Tsallis relative entropies.

In this paper, Ghabries-Abbas-Mourad log-majorization is generalized in two different cases.

. In this paper, we shall obtain extensions of Lemos-Soares log-majorization via Furuta inequality.

In this paper, we will obtain several log-majorization inequalities via Furuta inequalities with negative powers, which extends the related results before.

A Hiai-Lin type log-majorization, which is a simultaneous extension of [3, Corollary 3.1] and [4, Corollaries 3.3 and 3.4], is obtained via a block-matrix technique.

In this paper, we utilize the convexity of the function f(v) = parallel to vertical bar A(v)XB(1-v)vertical bar(r)parallel to.parallel to vertical bar A(1-v)XB(v)vertical bar(r)parallel to and the Hermite-Hadaniard inequality to obtain a family of new refinements of Cauchy-Schwarz norm inequality for operators, which extends the related results.

In this short paper, we show a Lemos-Soares type norm inequality, which extends the relative result before.

In this paper, we prove several extensions of Hiai-Lin type eigenvalue inequality which extends the relative result before.

In this paper, we will show the existence of positive semidefinite solution of Furuta type operator equation Sigma(n-1)(j-0) A(j)XA(n-j-1)=Y, where Y can be expressed by a comprehensive form.

In this paper, we shall prove that a grand Fujii-Fujii-Nakamoto operator inequality implies operator order and operator chaotic order under different conditions.

In this paper, we present several operator versions of the Hermite-Hadamard inequality for the operator convex function, which are refinements of some operator convex inequalities presented by Dragomir [

In this paper, we will show a generalized Matharu-Aujla log majorization inequality via an operator order preserving inequality, which extends the related results.

In this paper, we shall prove a log majorization inequality, which extends Furuta’s result. c ©2017 All rights reserved.

Let A, B and C be three positive definite matrices. In this paper, we show a characterization of A >= B >= C via the Karcher mean as follows,Lambda(omega;A(-p1),B-p2,B-t(sic)(s)C-p3) <= C, Lambda(omega;C-p1,B-p2,B-t(sic)(s)A(p3)) >= Ahold for t epsilon [0,1], s >= 1, p(1), p(2) > 0 and p(3) > 1, where (omega) over cap = (1/p1+1, 1/p2+1, 2/(p3-t) s+t-1), omega = (w(1), w(2), w(3)) = (omega) over cap/vertical bar vertical bar(omega) over cap vertical bar vertical bar(1).

We prove an extension of Furuta inequality with nonnegative powers for multi-operator. Then we show its application to Pedersen-Takesaki type operator equation. (C) 2016 All rights reserved.

uniqueness result of weak solution for the 3D viscous magneto-hydrodynamics equations in B^1_∞,∞ is proved by means of the Fourier localization technique and the losing derivative estimates.

The existence of positive semidefinite solutions ofthe operator equation $\displaystyle\sum_{j=1}^{n}A^{n-j}XA^{j-1}=Y$ is investigated by applying grand Furuta inequality. If there exists positive semidefinite solutions of the operator equation, one of the special types of Y is obtained, which extends the related result before. Finally, an example is given based on our result. Keywords: grand Furuta inequality, operator equation, matrix equation, positive semidefinite operator.