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A short note on a multiplier of the Nörlund means and convex maps of the unit disc

Ali Z. S.

Fasciculi Mathematici

2011

Nr 46

17--24

The problem of a multiplier !(n) of the Norlund means and convex maps of the unit disc is being considered again, but with a multiplier !(n) of dierent form then that appeared by Ziad S. Ali in [1]. With this we would have brought up again in a rather unied approach the results of G. Polya, and I.J. Schonberg in [7], T. Basgoze, J.L. Frank and F.R. Keogh in [3], and Ziad S. Ali in [2]. The new multiplier w(n) gives rise to interesting applications related to function expansion by the Chebychev polynomials of the rst and the second kind, an application to bionomial trigonometric formulas and an application to the subordination principle.