4,632 research outputs found

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

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    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

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

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

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

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    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

    A Functional Associated with Two Bounded Linear Operators in Hilbert Spaces and Related Inequalities

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    Inequalities for Stieltjes Integrals with Convex Integrators and Applications

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    Inequalities for a GrĆ¼ss type functional in terms of Stieltjes integrals with convex integrators are given. Applications to the ČebyÅ”ev functional are also provided

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

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    Some Jensenā€™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

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    Some inequalities related to the LupaŹ‚-Beesack-Pečarić result for m āˆ’ Ļˆ āˆ’convex and M āˆ’ Ļˆ āˆ’convex functions and applications are given

    A Generalisation of the Pečarić-Rajić Inequality in Normed Linear Spaces

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    Some Inequalities for the Relative Entropy and Applications

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    Some new inequalities for the relative entropy and applications are given

    A Note on Besselā€™s Inequality

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    A monotonicity property of Besselā€™s inequality in inner product spaces is given
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