New improvement of the converse Jensen inequality
نویسندگان
چکیده
منابع مشابه
A Converse of the Jensen Inequality for Convex Mappings of Several Variables and Applications
In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon’s and Rényi’s entropy mappings are also given.
متن کاملLetter to the Editor Remarks on “ On a Converse of Jensen ’ s Discrete Inequality ” of S .
holds see, e.g., 1, page 43 . If φ is strictly convex, then 1 is strict unless xi c for all i ∈ {j : pj > 0}. The following results are given in 2 . Theorem 1. Let I a, b , where a < b, x x1, . . . , xn ∈ I and p p1, . . . , pn , ∑n i 1 pi 1, be a sequence of positive weights associated with x. Let φ be a (strictly) positive, twice continuously differentiable function on I and 0 ≤ p, q ≤ 1, p q...
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We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi's inequality. The obtained results are then applied for establishing new mean-va...
متن کاملRemarks on “ On a Converse of Jensen ’ s Discrete Inequality ” of S .
holds see, e.g., 1, page 43 . If φ is strictly convex, then 1 is strict unless xi c for all i ∈ {j : pj > 0}. The following results are given in 2 . Theorem 1. Let I a, b , where a < b, x x1, . . . , xn ∈ I and p p1, . . . , pn , ∑n i 1 pi 1, be a sequence of positive weights associated with x. Let φ be a (strictly) positive, twice continuously differentiable function on I and 0 ≤ p, q ≤ 1, p q...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2018
ISSN: 1331-4343
DOI: 10.7153/mia-2018-21-17