The Basic Existence Theorem of Riemann-Stieltjes Integral

A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality

Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Loéve-Young inequality for the Riemann-Stieltjes integrals driven by irregular signals. Using this result we strengthen some results of Lyons on the existence of solutions of integral equatio...

The Riemann-stieltjes Integral on Time Scales

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given.

A Companion of Ostrowski’s Inequality for the Riemann-stieltjes Integral

On Approximation of the Riemann–stieltjes Integral and Applications

Several inequalities of Grüss type for the Stieltjes integral with various type of integrand and integrator are introduced. Some improvements inequalities are proved. Applications to the approximation problem of the Riemann–Stieltjes integral are also pointed out.

Existence and stability results for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations

Keywords: Volterra–Stieltjes integral equation Fractional integral–differential equations Riemann–Liouville fractional operators Existence and stability of solutions Fixed point a b s t r a c t Our aim in this paper is to study the existence and the stability of solutions for Riemann–Liouville Volterra–Stieltjes quadratic integral equations of fractional order. Our results are obtained by using...