Related papers: The Riemann-Stieltjes integral on time scales

We prove dynamic inequalities of majorisation type for functions on time scales. The results are obtained using the notion of Riemann-Stieltjes delta integral and give a generalization of [App. Math. Let. 22 (2009), no. 3, 416--421] to time…

Integrating with respect to functions which are constant on intervals whose bounds are discontinuity points (of those functions) is frequent in many branches of Mathematics, specially in stochastic processes. For such functions and alike…

In the theory of time scales, given $\mathbb{T}$ a time scale with at least two distinct elements, an integration theory is developed using ideas already well known as Riemann sums. Another, more daring, approach is to treat an integration…

We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we…

This paper presents Stieltjes-type integration for operator-valued functions with respect to spectral families. The relation between Riemann-Stieltjes integrals associated with some classes of spectral families including, in particular,…

We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.

We give the rate of convergence of some optimal lower Riemann-Stieltjes sums toward the integral.

In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.

We consider general formulations of the change of variable formula for the Riemann-Stieltjes integral, including the case when the substitution is not invertible.

We introduce more general concepts of Riemann-Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for existence and uniqueness of solution to an initial value…

The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.

Inter alia, we present a Fourier series involving the generalised Stieltjes constants.

The paper surveys the basic properties of generalized Stieltjes functions including some new ones. We introduce the notion of the exact Stieltjes order and give a criterion of exactness, simple sufficient conditions and some prototypical…

Time scales are a model of time, where the continuous and the discrete time cases are considered and merged into the same framework. In this paper some basic definitions of the time scale calculus are presented. Simultaneously, a package in…

In this paper, motivated by physical considerations, we introduce the notion of modified Riemann sums of Riemann-Stieltjes integrable functions, show that they converge, and compute them explicitely under various assumptions.

Using a concept of filter we propose one generalization of Riemann integral, that is integration with respect to filter. We study this problem, demonstrate different properties and phenomena of filter integration.

The Abel-Steffensen inequality is extended to the context of several variables. Applications to Fourier analysis of several variables and Riemann-Stieltjes integration are also included.

Some new integrals involving the Stieltjes constants are developed in this paper.

We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular…

Some new integrals involving the Stieltjes constants are developed in this paper.