Inequalities of Furuta and Mond-Pečarić on the Hadamard product.
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.
Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces and are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in is also shown.