منابع مشابه
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...
متن کاملA 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 کاملLevinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
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 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...
متن کاملJensen Inequality with Subdifferential for Sugeno Integral
The classical Jensen inequality for concave function φ is adapted for the Sugeno integral using the notion of the subdifferential. Some examples in the framework of the Lebesgue measure to illustrate the results are presented.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2009
ISSN: 0035-7596
DOI: 10.1216/rmj-2009-39-6-1905