Research Article

Moroccan Journal of Pure and Applied Analysis

, 2:7

First online:

Open Access

Bounds for the weighted Dragomir-Fedotov functional

• Mohammad W. AlomariAffiliated withDepartment of Mathematics, Faculty of Science and Information Technology,, Irbid National University Email author

Abstract

In literature the Dragomir-Fedotov functional is well known as
$$\mathcal{D}(f;u):=\int\limits_{a}^{b}{f(x)du}(x)-\frac{u(b)-u(a)}{b-a}\int\limits_{a}^{b}{f(t)}dt$$
.
In this work a generalization of D(f; u) is established. Namely, we define the weighted Dragomir-Fedotov functional such as:
$$\mathcal{O}\mathcal{D}(f,g;u):=\frac{1}{u(b)-u(a)}\cdot \int\limits_{a}^{b}{f(x)}du(x)-\frac{1}{\int\limits_{b}^{b}{g(t)dt}}\cdot \int\limits_{a}^{b}{f(t)}g(t)dt$$
, and hence several bounds are proved.

Key words and phrases

Grüuss inequality Riemann - Stieltjes integral functional