Riemann-Stieltjes integral


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Riemann-Stieltjes integral

[¦rē‚män ′stēl·tyəs ‚int·i·grəl]
(mathematics)
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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.
Braescu, A generalisation of the trapezoid rule for the Riemann-Stieltjes integral and applications, Nonlinear Anal.
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]).
1, and the corresponding Riemann-Stieltjes integral
Clearly, we can construct Riemann-Stieltjes integral for this j-dimensional problem similarly as above.
17) are also determined by the condition based on the Riemann-Stieltjes integral with the distribution function [[omega].
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.