A linear Riemann-Stieltjes integral equation system

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

Positive solutions for fractional differential equation involving the Riemann-Stieltjes integral conditions with two parameters

Through the application of the upper-lower solutions method and the fixed point theorem on cone, under certain conditions, we obtain that there exist appropriate regions of parameters in which the fractional differential equation has at least one or no positive solution. In the end, an example is worked out to illustrate our main results. c ©2016 All rights reserved.

Riemann-Stieltjes type integral based on generated pseudo-operations

We shall consider generated pseudo-operations of the following form: x⊕ y = g(−1) (g(x) + g(y)) , x ̄ y = g(−1) (g(x)g(y)) , where g is a positive strictly monotone generating function and g(−1) is its pseudo-inverse. Using this type of pseudo-operations, the Riemann-Stieltjes type integral will be introduced and investigated.

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.