The Cesàro-Perron-Stieltjes integral, I

The Strong Perron Integral

In this paper, we study the strong Perron integral, and show that the strong Perron integral is equivalent to the McShane integral.

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.

Inequalities for the Riemann-stieltjes Integral of S-dominated Integrators with Applications (i)

Assume that u; v : [a; b] ! R are monotonic nondecreasing on the interval [a; b] : We say that the complex-valued function h : [a; b] ! C is S-dominated by the pair (u; v) if jh (y) h (x)j 2 [u (y) u (x)] [v (y) v (x)] for any x; y 2 [a; b] : In this paper we show amongst other that Z b a f (t) dh (t) 2 Z b a jf (t)j du (t) Z b a jf (t)j dv (t) ; for any continuous function f : [a; b] ! C. Appl...

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

THE STRONG PERRON INTEGRAL IN THE n-DIMENSIONAL SPACE R

In this paper, we introduce the SP -integral and the SPα-integral defined on an interval in the n-dimensional Euclidean space Rn. We also investigate the relationship between these two integrals.