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...

Pulse code modulation is a widespread technique in digital communication with significant impact on existing modern and proposed future communication technologies. Its widespread utilization is due to its simplicity and attractive spectral characteristics. In this paper, we present a new approach to the spectral analysis of PCM signals using Riemann-Stieltjes integrals, which is very accurate f...

In this article, we study the oscillation of second order forced impulsive differential equation with γ-Laplacian and nonlinearities given by Riemann-Stieltjes integrals of the form

The Stieltjes constants γk(a) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about its only pole at s = 1. We present the relation of γk(1) to the ηj coefficients that appear in the Laurent expansion of the logarithmic derivative of the Riemann zeta function about its pole at s = 1. We obtain novel integral representations of the Stieltjes constants and new d...

Some new inequalities are obtained relating to the generalized trapezoid and midpoint rules for the Riemann–Stieltjes integral with a convex integrand and monotone nondecreasing integrator. Results are deduced for the special case of weighted Riemann integrals. Mathematics subject classification (2000): Primary 26D15, Secondary 26D10..

In this paper, we study the existence and nonexistence of positive solutions a system Riemann–Liouville fractional differential equations with ϱ-Laplacian operators, supplemented coupled nonlocal boundary conditions containing Riemann–Stieltjes integrals, derivatives various orders, parameters. We apply Schauder fixed point theorem in proof result.