Starting from a probability σ on the half-line with moments of any order A.G. Pakes has defined probabilities σr by length biasing of order r and gr by the stationary-excess operation of order r, r = 1, 2, . . . . Examples are given to show that σ can be determined in the Stieltjes sense while σ1 and g1 are indeterminate in the Stieltjes sense. This shows that a statement in a recent paper by P...

In this paper we introduce the interval-valued APHenstock-Stieltjes integral and investigate some properties of the these integrals.

We generalize Fejer?s theorem for Fourier-Stieltjes series of functions bounded variation.

This paper deals with the existence and global stability of solutions a new class Volterra partial integral equations Hadamard-Stieltjes fractional order.

RIEMANN AND RIEMANN-STIELTJES INTEGRABILITY Looking back over the notes already posted on this and related subjects, I felt that their organization did not emphasize the things that are important on the subject of the caption. Hence these notes, which will initially reprise things that are already treated in the others, but with different emphasis. The material on almost-everywhere continuity a...

Bounds are proved for the Stieltjes polynomial En+1, and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. Applying these results, convergence theorems are proved for the Lagrange interpolation process...

In this paper, we study some existence and uniqueness results for systems of differential equations in which each the system involves a different Stieltjes derivative. Specifically, show that problems can only have one solution under Osgood condition, or even, Montel–Tonelli condition. We also explore guaranteeing these conditions. Along way, obtain interesting properties Lebesgue–Stieltjes int...

Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also pointed out.

The classical Stieltjes transform is extended to a subspace of Boehmians. The transform is shown to be an analytic function in the half-plane Re z > 0. Some Abelian type theorems are established.