In this paper, we firstly obtain two identities for multiplicative differentiable functions. Then by using these identities, establish Ostrowski and Simpson type inequalities integrals. At the end give detail applications of our main results

Introduction/purpose: Certain integrals involving the generalized Mittag-Leffler function with different types of polynomials are established. Methods: The properties used in conjunction kinds such as Jacobi, Legendre, and Hermite order to evaluate their integrals. Results: Some integral formulae Legendre function, Bessel Maitland hypergeometric functions derived. Conclusions: results obtained ...

In this paper, using the identity proved [43]in for fractional integrals, some new Ostrowski type inequalities for Riemann-Liouville fractional integrals of functions of two variables are established. The established results in this paper generalize those results proved in [43].

Mock modular forms are central objects in the recent discoveries of new instances of Moonshine. In this paper, we discuss the construction of mixed mock modular forms via integrals of theta series associated to indefinite quadratic forms. In particular, in this geometric setting, we realize Zwegers’ mock theta functions of type ( p, 1) as line integrals in hyperbolic p-space.

Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x| are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map L → L for 1 < p < ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H1(Sn−1).

Using linearized superfields, R 4 terms in the Type II superstring effective action com-pactified on T 2 are constructed as integrals in N=2 D=8 superspace. The structure of these superspace integrals allows a simple proof of the R 4 non-renormalization theorems

This note presents techniques to analytically solve double integrals of the dilogarithmic type which are of great importance in the perturbative treatment of quantum-field theory. In our approach divergent integrals can be calculated similar to their convergent counterparts after identifying and isolating their singular parts.