Vol. 20, No. 2, 1967

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ISSN: 0030-8730
On the convergence of quasi-Hermite-Fejér interpolation

K. K. Mathur and R. B. Saxena

Vol. 20 (1967), No. 2, 245–259
Abstract

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

Sn(1,f) = f(1),Sn(xn⊳,f ) = f(xnν)1 ≦ ν ≦ n,Sn (− 1,f) = f(− 1)

and

S′n(xnν,f) = βnν1 ≦ ν ≦ n,

where β’s are arbitrary numbers; xn0 = 1,xnn+1 = 1 and {x} are the zeros of orthogonal polynomial system {pn(x)} belonging to the weight function (1 x2)p|x|q,0 < p 12, 0 < q < 1 (which actually vanishes at a point in the interval [1,+1]). Further it has been proved that quasi-conjugate pointsystem {X} (similar to Fejér conjugate pointsystem) belonging to the fundamental pointsystem {xnv} 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
Authors
K. K. Mathur
R. B. Saxena