Sharp Bounds for the Deviation of a Function from the Chord Generated by its Extremities and Applications

Sharp bounds for the deviation of a real-valued function f defined on a compact interval [a, b] to the chord generated by its end points (a, f (a)) and (b, f (b)) under various assumptions for f and f' including absolute continuity, convexity, bounded variation, monotonicity etc., are given. Some applications for weighted means and f-divergence measures in Information Theory are also provided

Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces

Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided

Refinements of the Hermite-Hadamard Integral Inequality for Log-Convex Functions

Two refinements of the classical Hermite-Hadamard integral inequality for log-convex functions and applications for special means are given

Inequalities for Stieltjes Integrals with Convex Integrators and Applications

Inequalities for a Grüss type functional in terms of Stieltjes integrals with convex integrators are given. Applications to the Čebyšev functional are also provided

Some Jensen's Type Inequalities for Twice Differentiable Functions of Selfadjoint Operators in Hilbert Spaces

Some Jensen’s type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided

On the Lupas-Beesack-Pecaric Inequality for Isotonic Linear Functionals

Some inequalities related to the Lupaʂ-Beesack-Pečarić result for m − ψ −convex and M − ψ −convex functions and applications are given

Some Inequalities for the Relative Entropy and Applications

Some new inequalities for the relative entropy and applications are given

A Note on Bessel’s Inequality

A monotonicity property of Bessel’s inequality in inner product spaces is given