On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation
نویسندگان
چکیده
Some Ostrowski type inequalities are given for the Stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation. The case when |f ′| is convex is explored. Applications for the midpoint rule and a generalised trapezoid type rule are also presented.
منابع مشابه
Ostrowski and trapezoid type inequalities for the Stieltjes integral with Lipschitzian integrands or integrators
Some Ostrowski and trapezoid type inequalities for the Stieltjes integral in the case of Lischitzian integrators for both Hölder continuous and monotoonic integrals are obtained. The dual case is also analysed. Applications for the midpoint rule are pointed out as well.
متن کاملOn the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications
In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.
متن کاملOstrowskis Type Inequalities for Complex Functions Dened on Unit Circle with Applications for Unitary Operators in Hilbert Spaces
Some Ostrowskis type inequalities for the Riemann-Stieltjes integral R b a f eit du (t) of continuous complex valued integrands f : C (0; 1)! C de ned on the complex unit circle C (0; 1) and various subclasses of integrators u : [a; b] [0; 2 ] ! C of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well. 1. Introduction The ...
متن کاملApproximating the Stieltjes Integral via the Darst-pollard Inequality
An approximation of the Stieltjes integral of bounded integrals and continuous integrators via the Darst-Pollard inequality is given. Applications for the generalised trapezoid formula and the Ostrowski inequality for functions of bounded variation are also provided.
متن کاملIntegration with Respect to Fractal Functions and Stochastic Calculus Ii
The link between fractional and stochastic calculus established in part I of this paper is investigated in more detail. We study a fractional integral operator extending the Lebesgue–Stieltjes integral and introduce a related concept of stochastic integral which is similar to the so–called forward integral in stochastic integration theory. The results are applied to ODE driven by fractal functi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Computers & Mathematics with Applications
دوره 54 شماره
صفحات -
تاریخ انتشار 2007