Approximation by polynomials and ridge functions of classes of \(s\)-monotone radial functions (Q927688)

The approximation by polynomials, ridge functions and radial functions is a central part of the work in this article. The order of approximation of polynomials and ridge functions is analysed with respect to the \(L_q\)-norm of \(s\)-monotone radial functions in \(L_p\). The spaces are defined with respect to an interval on the real line. Both upper as well as lower bounds are provided for all \(p\) and \(q\) in \([1,\infty]\). Therefore, the exact orders of approximation are established.