On the convergence of quasi-Hermite-Fejér interpolation

K. K. Mathur and R. B. Saxena

Vol. 20 (1967), No. 2, 245–259

DOI: 10.2140/pjm.1967.20.245

Abstract

The present paper deals with the convergence of quasiHermite-Fejér interpolation series {S_n(x,f)} satisfying the conditions

and

where β_nν’s are arbitrary numbers; x_n0 = 1,x_nn+1 = −1 and {x_nν} are the zeros of orthogonal polynomial system {p_n(x)} belonging to the weight function (1 − x²)^p|x|q,0 < p ≦, 0 < q < 1 (which actually vanishes at a point in the interval [−1,+1]). Further it has been proved that quasi-conjugate pointsystem {X_nν} (similar to Fejér conjugate pointsystem) belonging to the fundamental pointsystem {x_nv} lie everywhere thickly in the interval [−1,+1].

Mathematical Subject Classification

Primary: 41.10

Milestones

Received: 12 September 1962

Revised: 12 May 1964

Published: 1 February 1967