We introduce two subclasses T ∗(p, α, j) and C(p, α, j) (0 ≤ α < p − j + 1, 1 ≤ j ≤ p, p ∈ N = {1, 2, . . .}) of p-valent starlike and p-valent convex functions with negative coefficents. In this paper we obtain coefficient inequalities, distortion theorems, extreme points and integral operators for functions belonging to the classes T ∗(p, α, j) and C(p, α, j). We also determine the radii of c...

In this paper some new retarded integral inequalities are established and explicit bounds on the unknown functions are derived. The present results extend some existing ones proved by Lipovan in [A retarded integral inequality and its applications, J. Math. Anal. Appl. 285 (2003) 436-443].

Some new nonlinear retarded integral inequalities of Gronwall-like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No. 3, pp. 563–578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.

i.e., the supremum of all orders of torsion points on elliptic curves defined over some degree d number field. Write T (d)′ for the set of prime divisors of elements of Td, and P (d) for the largest element of T (d)′. Let TCM(d) (resp. TIM(d)) be the subset of T (d) corresponding to elliptic curves with complex multiplication (resp. with algebraic integral modulus j(E)), and similarly adding th...

The standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument |z|, and to use an asymptotic series for large |z|. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [1] derived a series for an exp-arc integral which gave rise to an absolutely convergent series for the J and I Bessel functions with integral order. Such ser...

Three-body resonances in atomic systems are calculated as complexenergy solutions of Faddeev-type integral equations. The homogeneous FaddeevMerkuriev integral equations are solved by approximating the potential terms in a Coulomb-Sturmian basis. The Coulomb-Sturmian matrix elements of the three-body Coulomb Green’s operator has been calculated as a contour integral of two-body Coulomb Green’s ...

New results and new applications of fractional calculus for continuous random variables are presented. Some classical integral results are also generalized. On the other hand, some results (corollaries) on the paper [Fractional integral inequalities for continuous random variables, Malaya J. Mat. 2(2014), 172–179] are corrected.

To estimate a multiple integral of a function over the unit cube, Haber proposed two Monte Carlo estimators /'j and J'2 based on 2N and 4N observations, respec2 2 » tively, of the function. He also considered estimators Dy and D2 of the variances of/j and J'2, respectively. This paper shows that all these estimators are asymptotically normally distributed as N tends to infinity.

We present a robust integral equation method for the calculation of the electrostatic and thermal properties of systems made of piecewise homogeneous, high contrast materials. By high contrast, we mean that the electrical or thermal conductivity ratios are high. Our approach involves a modification of the standard integral representation using, in electrostatic terms, the polarization charge as...