The Markov–Bernstein inequality and Hermite–Fejér interpolation for exponential-type weights Original Research Article

We investigate the coefficients of Hermite–Fejér interpolation polynomials based at zeros of orthogonal polynomials with respect to exponential-type weights. First, we obtain the modified Markov–Bernstein inequalities with respect to View the MathML sourcew∈F(Lip12). Then using the modified Markov–Bernstein inequalities, we estimate the value of View the MathML source|pn(r)(wρ2,x)/pn′(wρ2,x)| for r=1,2,…r=1,2,… at zeros of View the MathML sourcepn(wρ2;x) and we apply this to estimate the coefficients of Hermite–Fejér interpolation polynomials. Here, View the MathML sourcepn(wρ2,x) denotes the nnth orthogonal polynomial with respect to an exponential-type weight wρ(x)=|x|ρw(x)wρ(x)=|x|ρw(x), x∈Rx∈R, ρ>−1/2ρ>−1/2.