83 research outputs found
On inequalities of Jensen-Ostrowski type
We provide new inequalities of Jensen-Ostrowski type, by considering bounds for the magnitude of (Formula Presented), with various assumptions on the absolutely continuous function f:[a,b]âC and a ÎŒ-measurable function g, and a complex number λ. Inequalities of Ostrowski and Jensen type are obtained as special cases, by setting λ=0 and ζ=â«Î©gdÎŒ, respectively. In particular, we obtain some bounds for the discrepancy in Jensenâs integral inequality. Applications of these inequalities for f-divergence measures are also given
JensenâOstrowski inequalities and integration schemes via the Darboux expansion
By using the Darboux formula obtained as a generalization of the Taylor formula, we deduce some JensenâOstrowski-type inequalities. The applications to quadrature rules and f-divergence measures (specifically, for higher-order Ï-divergence) are also presented.http://link.springer.com/journal/11253hj2019Mathematics and Applied Mathematic
Jensen and Ostrowski type inequalities for general Lebesgue integral with applications
Some inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for f-divergence measure are provided as well
General Lebesgue integral inequalities of Jensen and Ostrowski type for differentiable functions whose derivatives in absolute value are h-convex and applications
Some inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral of differentiable functions whose derivatives in absolute value are h-convex are obtained. Applications for f-divergence measure are provided as well
Series of divergence measures of type k, information inequalities and particular cases
Information and Divergence measures deals with the study of problems concerning information processing, information storage, information retrieval and decision making. The purpose of this paper is to find a new series of divergence measures and their applications, discuss the mathematical tools for finding convexity of the functions. Applications of convex functions in information theory, relationship between new and well-known divergence measures are discussed. Also some new bounds have been established for divergence measures using new f divergence measures and its properties
Combinatorial extensions of Popoviciu\u27s inequality via Abel-Gontscharoff polynomial with applications in information theory
We establish new refinements and improvements of Popoviciuâs inequality for n-convex functions using Abel-Gontscharoff interpolating polynomial along with the aid of new Green functions. We construct new inequalities for n-convex functions and compute new upper bounds for Ostrowski and GrĂŒss type inequalities. As an application of our work in information theory, we give new estimations for Shannon, Relative and Zipf-Mandelbrot entropies using generalized Popoviciuâs inequality
Inequality for power series with nonnegative coefficients and applications
We establish in this paper some Jensenâs type inequalities for functions defined by power series with
nonnegative coefficients. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided
as well
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