Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Some rules, based on Turán quadrature formulas, are derived for the numerical evaluation of one-dimensional Cauchy principal value integrals, and theorems on the convergence of a sequence of such rules are given. [ABSTRACT FROM AUTHOR]
A method is considered for constructing weighted arithmetic means from IR to IR, which possess the interpolation property. Necessary and sufficient conditions are then given in order to solve the convergence problem to a continuous real function f(ξ), ξ∈IR of such interpolating mean functions. Finally a few formulas are considered as an application of the proposed method. [ABSTRACT FROM AUTHOR]