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New sharp inequalities of Ostrowski and generalized trapezoid type for the Riemann-Stieltjes integrals and applications (1408.1497v1)
Published 7 Aug 2014 in math.CA
Abstract: In this paper, new sharp weighted generalizations of Ostrowski and generalized trapezoid type inequalities for the Riemann--Stieltjes integrals are proved. Several related inequalities are deduced and investigated. New Simpson's type inequalities for $\mathcal{RS}$--integral are pointed out. Finally, as application; an error estimation of a general quadrature rule for $\mathcal{RS}$--integral via Ostrowski--generalized trapezoid quadrature formula is given.
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