A Chebyshev-type quadrature for a probability measure σ is a distribution which is uniform on n points and has the same first k moments as σ. We give bounds for the smallest possible n required to achieve a certain degree k. In contrast to previous results of this type, our bounds use only simple properties of σ and are thus applicable in wide generality. In particular, it is shown that wheneve...

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...

Equal-weight integration rules are studied in the context of certain families of Hubert spaces of analytic functions defined in a family of confocal ellipses containing the interval of integration. Rules which minimize the norm of the error functional in these spaces are shown to exist and several such rules are tabulated. Asymptotic properties of these rules are studied for ellipses shrinking ...

background exploring changes in health inequality and its determinants over time is of policy interest. accordingly, this study aimed to decompose inequality in neonatal mortality into its contributing factors and then explore changes from 1995-2000 to 2005-2010 in iran.   methods required data were drawn from two iran’s demographic and health survey (dhs) conducted in 2000 and 2010. normalized...