The Jensen inequality in an external formula
نویسندگان
چکیده
منابع مشابه
Sobolev 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...
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 کاملOn 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 type inequality for generalized Sugeno integral
We prove necessary and sufficient conditions for the validity of Jensen type inequalities for generalized Sugeno integral. Our proofs make no appeal to the continuity of neither the fuzzy measure nor the operators. For several choices of operators, we characterize the classes of functions for which the corresponding inequalities are satisfied.
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2012
ISSN: 1846-579X
DOI: 10.7153/jmi-06-44