Refinement of Jensen’s inequality and estimation of f- and Rényi divergence via Montgomery identity [PDF]
Journal of Inequalities and Applications, 2018 Jensen’s inequality is important for obtaining inequalities for divergence between probability distribution. By applying a refinement of Jensen’s inequality (Horváth et al. in Math. Inequal. Appl.
Khuram Ali Khan +3 more
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Refinement of the Jensen integral inequality [PDF]
Open Mathematics, 2016 In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.
Sever Dragomir Silvestru +2 more
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On generalization of refinement of Jensen’s inequality using Fink’s identity and Abel-Gontscharoff Green function [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the ‘two-point right focal’ problem. We use Fink’s identity and a new Abel-Gontscharoff-type Green’s function for a ‘two-point right focal’ to generalize ...
Tasadduq Niaz +2 more
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Jensen’s inequality and tgs-convex functions with applications [PDF]
Journal of Mahani Mathematical Research, 2023 In recent years, many researches have been done on the tgs-convex functions and their applications. In this article, we present some properties of the tgs-convex functions by interesting examples.
Hasan Barsam +2 more
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Extended Jensen’s functional for diamond integral via Green’s function and Hermite polynomial
Journal of Inequalities and Applications, 2022 In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension of Jensen’s functional for n-convex functions is deduced from Jensen’s inequality involving diamond integrals.
Fazilat Bibi +3 more
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Extended Jensen’s Functional for Diamond Integral via Hermite Polynomial
Journal of Function Spaces, 2021 In this paper, with the help of Hermite interpolating polynomial, extension of Jensen’s functional for n-convex function is deduced from Jensen’s inequality involving diamond integrals.
Rabia Bibi +3 more
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Refinements of the integral Jensen’s inequality generated by finite or infinite permutations
Journal of Inequalities and Applications, 2021 There are a lot of papers dealing with applications of the so-called cyclic refinement of the discrete Jensen’s inequality. A significant generalization of the cyclic refinement, based on combinatorial considerations, has recently been discovered by the ...
László Horváth
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Uniform Treatment of Jensen’s Inequality by Montgomery Identity
Journal of Mathematics, 2021 We generalize Jensen’s integral inequality for real Stieltjes measure by using Montgomery identity under the effect of n−convex functions; also, we give different versions of Jensen’s discrete inequality along with its converses for real weights.
Tahir Rasheed +4 more
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A Refined Jensen Inequality Connected to an Arbitrary Positive Finite Sequence
Mathematics, 2022 The prime purpose of this paper is to provide a refinement of Jensen’s inequality in connection with a positive finite sequence. We deal with the refinement for particular cases and point out the relation between the new result with earlier results of ...
Shanhe Wu +3 more
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A new refinement of Jensen’s inequality with applications in information theory
Open Mathematics, 2020 In this paper, we present a new refinement of Jensen’s inequality with applications in information theory. The refinement of Jensen’s inequality is obtained based on the general functional in the work of Popescu et al.
Xiao Lei, Lu Guoxiang
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