Inequalities of Ostrowski type and applications in numerical integration.
Some new inequalities of Ostrowski-Grüss type are derived. They are applied to the error analysis for some Gaussian and Gaussian-like quadrature formulas.
We establish in this paper some Jensen’s type inequalities for functions defined by power series with nonnegative coefficients. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well.
Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.
For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from into . For more general operators of Hardy type, norm inequalities are proved which extend to weighted amalgams known estimates in weighted -spaces. Amalgams of the form , 1 < p,q < ∞ , q ≠ p, , are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.