[PDF] Top 20 A refinement of the integral form of Jensen’s inequality
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A refinement of the integral form of Jensen’s inequality
... In this paper, such a refinement of () is obtained. The results not only extend and gener- alize earlier results, but give a new method to refine inequality (). Moreover, the integral versions of classical ... See full document
19
A monotonic refinement of Levinson’s inequality
... Levinson’s inequality in a similar way that convex functions are characterized by Jensen’s ...Jensen’s inequality and proved their monotonicity and convexity ... See full document
7
Convex function and its secant
... The main results are related to Jensen’s inequality, its generalizations and refinements. As mentioned in the Introduction, Jensen has proved his inequality by applying mathematical in- duction. On ... See full document
15
Interpolations of Jensen's Integral Inequality
... We shall lean heavily on this probabilistic formulation both for compact notation within our proofs and for streamlining the algebra involved in them. The assump- tions of Theorem 1 are presumed throughout without ... See full document
11
On Solvability of the Nonlinear Optimal Control Problem for Processes Described by the Semi-linear Parabolic Equations
... nonlinear integral criterion of quality is ...nonlinear integral equation with additional condition in the form of the differential inequality, and the algorithm to determination of the ... See full document
6
A generalized form of Grüss type inequality and other integral inequalities
... Jensen’s inequality, in the sense of gener- alizations of the integral arithmetic mean and variance, can also be found in [], page ...Jensen’s inequality) Let (X, ; μ) be a finite measure space and ... See full document
18
Some new estimates of the ‘Jensen gap’
... holds. This inequality can be traced back to Jensen’s original papers [, ] and is one of the most fundamental mathematical inequalities. One reason for that is that in fact a great number of classical ... See full document
9
Symmetric Rogers-Hölder's inequalities on diamond-α calculus
... weighted form on dynamic time scales which was initiated by Stefan Hilger given in ...Discrete form of H¨ older’s inequality is given in [12] and found separately by Rogers and H¨ ...older. ... See full document
11
A refinement of Sándor Tóth's inequality
... include Jensen type inequalities [1], the general varia- tional inequality problem [2], delay integral inequalities [3], inequalities that involve higher-order partial derivatives [4] or harmonic ... See full document
11
On the refinements of the Jensen Steffensen inequality
... In this paper, we present a new refinement of the Jensen-Steffensen inequality, related to Theorem 1.3. Further, we investigate the log-convexity and the exponential convexity of functionals defined ... See full document
11
Integral Inequality of Hardy Type on Time Scales
... modified form leads to some extensions, variants and a new generalization of a class of inequalities which are related to Hardy’s and Opial’s integral ... See full document
10
Refinement of the Jensen integral inequality
... The Jensen inequality for convex functions plays a crucial role in the Theory of Inequalities due to the fact that other inequalities such as the arithmetic mean-geometric mean inequality, the Hölder ... See full document
8
An equivalent condition to the Jensen inequality for the generalized Sugeno integral
... Sugeno integral were introduced and initially examined by Sugeno ...Sugeno integral and proved a monotone convergence theorem for the Sugeno integral; Román-Flores et ...Sugeno integral and ... See full document
11
On the refinements of the integral Jensen Steffensen inequality
... Remark . It follows that a function is log-convex in the Jensen sense if and only if it is -exponentially convex in the Jensen sense. Also, by using the basic convexity theory, a function is log-convex ... See full document
18
Some remarks on Niezgoda's extension of Jensen-Mercer inequality
... Niezgoda’s inequality. The third section deals with the refinement of the result which is stated in the second ...the refinement of the Niezgoda’s ... See full document
11
Estimation of unknown function of nonlinear weakly singular integral inequalities of Gronwall–Bellman–Pachpatte type
... The aim of this paper is to extend certain results that were proved in [9, 10], and general- ize (1)–(4) to some weakly singular integral inequalities. The upper bound estimations of the unknown functions are ... See full document
16
Some New Inequalities of Qi Type for Definite Integrals
... mathematician- s and articles devoted to generalizing and applying the integral inequality ...Jensen’s inequality [6], convexity method [4], functional inequalities in abstract spaces [1, 4, ... See full document
7
A General Generalization of Jordan's Inequality and a Refinement of L. Yang's Inequality
... Jordan’s inequality: Refinements, generalizations, applications and related problems, B` udˇengsh`ı Y¯ anji¯ u T¯ ongx` un (Communications in Studies on Inequalities) 13 (2006), ... See full document
8
Inequalities of uncertain set with its applications
... An uncertain set, as a generalization of the uncertain variable, is a set-valued function on an uncertainty space. It provides theoretical foundations for uncertain inference and uncertain logic. This paper aims at ... See full document
10
Superadditivity of Some Functionals Associated to Jensen's Inequality for Convex Functions on Linear Spaces with Applications
... The Jensen inequality for convex functions plays a crucial role in the Theory of Inequalities due to the fact that other inequalities such as the generalised triangle inequality, the arithmetic ... See full document
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