Inequalities on the variances of convex functions of random variables.
Inequalities related to majorization of vectors.
Inequalities related to rearrangements of powers and symmetric polynomials.
Inequalities related to the Chebyshev functional involving integrals over different intervals.
Inequalities via convex functions.
Inequality between sides and diagonals of a space -gon and its integral analog
Inequality for power series with nonnegative coefficients and applications
We establish in this paper some Jensen’s type inequalities for functions defined by power series with nonnegative coefficients. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well.
Integral inequalities and computer algebra systems.
Integral inequalities involving generalized Erdélyi-Kober fractional integral operators
Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.
Integral inequalities of Gronwall type for piecewise continuous functions.
Integral inequalities of the Ostrowski type.
Integral inequalities related to Hardy's inequality.
Integral inequalities similar to Gronwall inequality.
Integral operators and weighted amalgams
For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from into . For more general operators of Hardy type, norm inequalities are proved which extend to weighted amalgams known estimates in weighted -spaces. Amalgams of the form , 1 < p,q < ∞ , q ≠ p, , are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.
Integral Representations of Functional Series with Members Containing Jacobi Polynomials
MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi polynomials.
Integralungleichungen aus der Hilbertraum-Theorie.
Integrodifferential inequality for stability of singularly perturbed impulsive delay integrodifferential equations.
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry.
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide criteria for these Sobolev type inequalities and for related properties. In particular, we implement in the context of probability measures the ideas of Maz'ja's capacity theory, and present equivalent forms relating the capacity of sets to their measure. Orlicz hypercontractivity efficiently describes the...
Inverse Limit Spaces Satisfying a Poincaré Inequality
We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces,...
Inverses of new Hilbert-Pachpatte-type inequalities.