In this paper, the authors give a new identity for Hadamard fractional integrals. By using of this identity, the authors obtain new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for (α,m)-GA-convex functions via Hadamard fractional integrals.

In this paper, some estimates of third and fourth inequalities in Hermite–Hadamard-type for coordinated convex functions are proved using the non-additivity integrals Fubini’s theorem fuzzy integrals. That is, results obtained context Lebesgue measure. Several examples provided on how to evaluate these order illustrate results.

In this paper we propose a new approach to fuzzy stochastic integrals of Itô and Aumann type. Then a fuzzy equation with fuzzy stochastic integrals is investigated. The existence and uniqueness of solution is proven. Some typical properties of the solution are also obtained. Similar results to set-valued stochastic integral equations are stated.

Convolution type Calderr on-Zygmund singular integral operators with rough kernels p.v. (x)=jxj n are studied. A condition on implying that the corresponding singular integrals and maximal singular integrals map L p ! L p for 1 < p < 1 is obtained. This condition is shown to be diierent from the condition 2 H 1 (S n?1).

We derive conditional Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain conditional Stein approximation bounds for multiple stochastic integrals and quadratic Brownian functionals.

The three-loop four-point function of stress-tensor multiplets in N = 4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by ...

in this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. the method is applied to a few test examples to illustrate the accuracy and the implementation of the method

In our previous work [8], we laid general foundations for motivic integration of constructible functions. One of the most salient features of motivic constructible functions is that they form a class which is stable by direct image and that motivic integrals of constructible functions depending on parameters are constructible as functions of the parameters. Though motivic constructible function...

We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as ...

We compute the lowest components of the Type II Ramond-Ramond boundary state for the tachyon profile T (X) = λe / √ 2 by direct path integral evaluation. The calculation is made possible by noting that the integrals involved in the requisite disk one-point functions reduce to integrals over the product group manifold U(n)× U(m). We further note that one-point functions of more general closed st...