On a Multiplier of the Progressive Means and Convex Maps of the Unit Disc
نویسندگان
چکیده
Abstract. In this paper we are concerned with a multiplier ω(n) of the Progressive means, and convex maps of the unit disc. With this concern we would have brought up in a rather unified approach the results of G. Pólya and I. J. Schoenberg in [7], T. Başgöze, J. L. Frank, and F. R. Keogh in [3], and Ziad S. Ali in [1]. More theorems on the properties of the multiplier ω(n) are given, and a key lemma showing combinatorial trigonometric identities whose offsprings are: Several combinatorial, and combinatorial trigonometric identities, and a new method for generating the Chebyshev’s polynomials. Finally we present a different form of ω(n) as well as relating ω(n) to the subordination principle.
منابع مشابه
On a Combinatorial Multiplier of the Extended Progressive Means and Convex Maps of the Unit Disc
In this paper, we generalize the ordinary basic model of the Progressive means by introducing the new notion of the extended Progressive means or the notion of the Progressive means with a moving sequence of partial sums. Afterwords we use this new concept to talk about a multiplier ωe(n, r, z, f) of the extended Progressive means and convex maps of the unit disk. The work presented gives more ...
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