A refined discrete Hilbert inequality obtained via the Hermite–Hadamard inequality

AbstractIn this paper we establish a general method for improving the discrete Hilbert-type inequalities via the Hermite–Hadamard inequality. The general result is then applied to homogeneous kernels. Moreover, some particular homogeneous kernels are considered, and a whole series of refinements of some recent results known from the literature are yielded. In addition some particular non-homogeneous cases are also considered

Superadditivity, Monotonicity, and Exponential Convexity of the Petrović-Type Functionals

We consider functionals derived from Petrović-type inequalities and establish their superadditivity, subadditivity, and monotonicity properties on the corresponding real n-tuples. By virtue of established results we also define some related functionals and investigate their properties regarding exponential convexity. Finally, the general results are then applied to some particular settings

Eigenvalue inequalities for differences of means of Hilbert space operators

AbstractWe prove several eigenvalue inequalities for the differences of various means of two positive invertible operators A and B on a separable Hilbert space, under the assumption that A-B is compact. Equality conditions of these inequalities are also obtained

Superadditivity, Monotonicity, and Exponential Convexity of the Petrović-Type Functionals

We consider functionals derived from Petrović-type inequalities and establish their superadditivity, subadditivity, and monotonicity properties on the corresponding real n-tuples. By virtue of established results we also define some related functionals and investigate their properties regarding exponential convexity. Finally, the general results are then applied to some particular settings