arXiv subjects

S. Malekinejad

Publications and source records attributed to S. Malekinejad.

3 recordsLinked to original sources

arXiv2023

Some Hadamard product inequalities for accretive matrices

In this paper, we obtain some new matrix inequalities involving Hadamard product. Also some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps and matrix concave functions are investigated. Among other results, it is shown that if $A, B, C, D$ are $n\times n$ positive definite matrices, then \begin{equation*} \left(αA+βB\right)^r\circ\left(αC+βD\right)^{1-r}\leq α\left(A^r\circ C^{1-r}\right)+β\left(B^r\circ D^{1-r}\right), \end{equation*} where $r \in (-1, 0) \cup (1, 2)$ and $" \circ "$ stands for the Hadamard product.

math.FA↗

arXiv2023

Operator mean inequalities for sector matrices

In this note, some inequalities involving operator means of sectorial matrices are proved which are generalizations and refinements of previous known results. Among them, let $A$ and $B$ be two accretive matrices with $A,B\in\mathcal{S}_θ$, $0 < mI \leqslant A, B \leqslant MI$ for positive real numbers $ M, m, \, σ$ be an operator mean and $σ^{*}$ be the adjoint mean of $ σ.$ If $σ^*\leqslant σ_1,σ_2\leqslant σ$ and $Φ$ is a positive unital linear map, then $$Φ^{p}\Re(A σ_{1} B) \leqslant \sec^{2p}θα^{p} Φ^{p}\Re(A σ_{2} B),$$ where $$ α= \max \left \lbrace K, 4^{1-\frac{2}{p}}K \right \rbrace,$$ and $ K= \frac{(M+m)^2}{4mM}$ is the Kantorovich constant.

math.FA↗

arXiv2017

Some new inequalities involving Heinz operator means

We give some new refinements of Heinz inequality and an improvement of the reverse Young's inequality for scalars and we use them to establish new inequalities for operators and the Hilbert-Schmidt norm of matrices. We give a uniformly and abbreviated form of the inequalities presented by Kittaneh and Mansarah, and the inequalities presented by Kai and we obtain some of their operator and matrix versions.

math.FA↗