منابع مشابه
On the refinements of the Jensen-Steffensen inequality
* Correspondence: [email protected] Abdus Salam School of Mathematical Sciences, GC University, 68-b, New Muslim Town, Lahore 54600, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we extend some old and give some new refinements of the JensenSteffensen inequality. Further, we investigate the log-convexity and the exponential conve...
متن کاملOn the Jensen-Steffensen inequality for generalized convex functions
Jensen–Steffensen type inequalities for P -convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen–Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.
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Steffensen’s inequality deals with the comparison between integrals over a whole interval [a, b] and integrals over a subset of [a, b]. In this paper we prove an inequality which is similar to Steffensen’s inequality. The most general form of this inequality deals with integrals over a measure space. We also consider the discrete case.
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.
متن کاملSobolev Regularity and an Enhanced Jensen Inequality
We derive a new criterion for a real-valued function u to be in the Sobolev space W 1,2(Rn). This criterion consists of comparing the value of a functional R f(u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values converges to zero as the convolutions approach u, and we prove that the rate of convergence to zero is connected...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 1998
ISSN: 1331-4343
DOI: 10.7153/mia-01-38