Riemann-Stieltjes integral


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Riemann-Stieltjes integral

[¦rē‚män ′stēl·tyəs ‚int·i·grəl]
(mathematics)
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Clearly, the Riemann-Stieltjes integral boundary conditions includes multipoint boundary conditions as special cases.
The Riemann-Stieltjes integral of y, with respect to [xi], is defined as
If f is bounded on [a, b], the for any t [member of] [a, b], the Riemann-Stieltjes Integral [[integral].
Dragomir, On the Ostrowski's inequality for Riemann-Stieltjes integral, Korean J.
Fedotov, An inequality of Gruss type for Riemann-Stieltjes integral and applications for special means, Tamkang J.
It is interesting to note that the relationship of the CG method to the Riemann-Stieltjes integral and Gauss quadrature was described in detail in [24, Section 14], but without any link to error estimation.
Using the orthogonality of the residuals, these algorithms are related to sequences of orthogonal polynomials, where the inner product is defined by a Riemann-Stieltjes integral with some particular distribution function [omega]([lambda]).
Here, A denotes a linear functional on C(J) given by Riemann-Stieltjes integral
Xiao starts by describing sets, relations, functions, cardinals, ordinals, reals, basic theorems and sequence limits, proceeding to Riemann integrals, Riemann-Stieltjes integrals, Lebesque-Radon-Stieltjes integrals, metric spaces, continuous maps, normed linear spaces, Banach spaces via operators and functionals, and Hilbert spaces and their operators.
are nondecreasing functions of bounded variation and the integrals are the Riemann-Stieltjes integrals.
To our knowledge, very few authors studied the existence result of positive solution for p-Laplacian fractional order differential systems with boundary conditions involving the Riemann-Stieltjes integrals.