On a Theorem by Bojanov and Naidenov applied to families of Gegenbauer-Sobolev polynomials

Abstract

n,λ } n≥0 be the sequence of monic orthogonal polynomials with respect the Gegenbauer-Sobolev inner productwhere α > − 1 2 and λ ≥ 0. In this paper we use a recent result due to B.D. Bojanov and N. Naidenov [3], in order to study the maximization of a local extremum of the kth derivative, where M n,λ is a suitable value such that all zeros of the polynomialn,λ attains its maximal value at the end-points of such interval. Also, some illustrative numerical examples are presented.