A Short Note on a Multiplier of the Nörlund Means and Convex Maps of the Unit Disc
نویسنده
چکیده
The problem of a multiplier ω(n) of the Nörlund means and convex maps of the unit disc is being considered again, but with a multiplier ω(n) of different form then that appeared by Ziad S. Ali in [1]. With this we would have brought up again in a rather unified approach the results of G. Pólya, 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 first and the second kind, an application to bionomial trigonometric formulas and an application to the subordination principle.
منابع مشابه
A note on a multiplier of the Norlund means and convex maps of the unit disc
Important and interesting results which are already known such as those by Pólya and Schoenberg in (1958), Başgöze et al. in (1970), and Ali in (1973), and which are related to convex maps of the unit disc are presented in this note by a more general, unified, and different method. The method considers the product of a nontrivial multiplier with the Norlund means, and shows how the known result...
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