Converses of the Jensen inequality derived from the Green functions with applications in information theory |
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| Authors: | Shahid Khan Muhammad Adil Khan Yu-Ming Chu |
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| Institution: | 1. Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan;2. Department of Mathematics, Huzhou University, Huzhou 313000, China |
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| Abstract: | Jensen integral inequality has got much importance regarding their applications in different fields of mathematics. In this paper, two converses of Jensen integral inequality for convex function are obtained. The results are applied to establish converses of Hölder and Hermite-Hadamard inequalities as well. At the end, some useful applications in information theory of the obtained results are given. The idea used in this paper may inculcate further research. |
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| Keywords: | convex function Csiszár divergence Green functions Jensen inequality |
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