New Improvements of the Jensen–Mercer Inequality for Strongly Convex Functions with Applications
In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known r...
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| Vydáno v: | Axioms Ročník 13; číslo 8; s. 553 |
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01.08.2024
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| Abstract | In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known results about strongly convex functions. We are also focused on important applications of the derived results in information theory, deducing estimates for χ-divergence, Kullback–Leibler divergence, Hellinger distance, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence. Additionally, we prove some applications to Mercer-type power means at the end. |
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| AbstractList | In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known results about strongly convex functions. We are also focused on important applications of the derived results in information theory, deducing estimates for χ-divergence, Kullback–Leibler divergence, Hellinger distance, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence. Additionally, we prove some applications to Mercer-type power means at the end. |
| Audience | Academic |
| Author | Mahmoud, Haitham Abbas Adil Khan, Muhammad Ivelić Bradanović, Slavica |
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| SubjectTerms | Convex analysis convex and strongly convex functions Convex functions Inequalities (Mathematics) Inequality Information theory Jensen inequality Jensen–Mercer inequality Mathematical optimization strong f-divergences |
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| Title | New Improvements of the Jensen–Mercer Inequality for Strongly Convex Functions with Applications |
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