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 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

On Some Discrete Inequalities in Normed Linear Spaces

Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given

Some Inequalities for Functions of Bounded Variation with Applications to Landau Type Results

Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p−norm for p Є [1,∞] are established. Applications related to the celebrated Landau inequality between the norms of the derivatives of a function are also pointed out

The Perturbed Median Principle for Integral Inequalities with Applications

In this paper a perturbed version of the Median Principle introduced by the author in 'The median principle for inequalities and applications' is developed. Applications for various Riemann- Stieltjes integral and Lebesgue integral inequalities are also provided

Some Inequalities for Power Series of Selfadjoint Operators in Hilbert Spaces via Reverses of the Schwarz Inequality

In this paper we obtain some operator inequalities for functions defined by power series with real coefficients and, more specifically, with non- negative coefficients. In order to obtain these inequalities some recent reverses of the Schwarz inequality for vectors in inner product spaces are utilized. Natural applications for some elementary functions of interest are also provided

Some Integral Inequalities of Grüss Type

Some classical and new integral inequalities of Grüss type are presented

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