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

• Autorzy: Ali Z. S.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Nörlund; Cesaro; de la Vallee-Poussin means; convex maps; combinatorial identities; Fourier series

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2011
• Tom: Nr 46
• Strony: 17--24
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Ali Z. S.

Bibliografia

• [1] Ali Z.S., A note on a multiplier of the Nörlund means and convex maps of the unit disc, International Journal of Mathematics and Mathematical Sciences (IJMMS), December 20(11)(2005), 3351-3357.
• [2] Ali Z.S., Convexity of Nörlund and progressive means, Indian Journal of Mathematics, May 15(2)(1973).
• [3] Basgoze T., Frank J.L., Keogh F.R., On convex univalent functions, Canadian Journal of Mathematics, 22(1970), 123-127.
• [4] Duren P.L., Univalent Functions, Springer-Verlag, Berlin and NewYork, (1983).
• [5] Hardy G.H., Divergent Series, Oxford Uni. Press, 1949.
• [6] Mathai A.M., A Handbook of Generalized Special Functions for statistical and physical sciences, Oxford Science Publications, 1993.
• [7] Pólya G., Schonberg I.J., Remarks on the de la Vallee Poussin means and convex conformal maps of the circle, Pacific J. Math., 8(1958), 295-334.