Improvement of Furuta’s Inequality with Applications to Numerical Radius

On the Numerical Radius and Its Applications*

We give a brief account of the numerical radius of a linear bounded operator on a Hilbert space and some of its better-known properties. Both finiteand infinitedimensional aspects are discussed, as well as applications to stability theory of finite-difference approximations for hyperbolic initial-value problems. 1. DEFINITION, BOUNDS, AND EVALUATION Let H be a Hilbert space over the complex fie...

Some numerical radius inequalities with positive definite functions

 ‎Using several examples of positive definite functions‎, ‎some inequalities for the numerical radius of‎ ‎matrices are investigated‎. ‎Also‎, ‎some open problems are stated‎.

Some improvements of numerical radius inequalities via Specht’s ratio

We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follow...

Improvement of Aczél’s Inequality and Popoviciu’s Inequality

On the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications

In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.