In this article we study the Heinz and Hermite-Hadamard inequalities. We derive whole series of refinements these inequalities involving unitarily invariant norms, which improve some recent results, known from literature. We also prove that if $A , B, X\in M_n(\mathbb{C})$ such $A$ $B$ are positive definite $f$ is an operator monotone function on $(0,\infty)$. Then \begin{equation*} |||f(A)X-...

We prove some results on operator equalities and inequalities involving positive maps, operator means and shorted operators. Inequalities for shorted operators involving convex operator functions and tensor product have also been proved.

In this paper we prove certain inequalities involving matrices and operators on Hilbert spaces. In particular inequalities involving the trace and the determinant of the product of certain positive definite matrices.