On a Combinatorial Multiplier of the Extended Progressive Means and Convex Maps of the Unit Disc
نویسنده
چکیده
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 light to what was presented by Ziad S.Ali in [1], and [2]. The cause of our new extended Progressive means is du to the fact that we are defining a different, and rather a more generalized sequence q j then the sequence q (n,r) j defined by Ziad S. Ali in [2]. We will also answer to the general question related to the role of monoticity of the sequence defining a Progressive sum on the statement “ a Progressive sum of a function f regular in the unit disc D = {z : z < 1} takes values in a convex domain iff f takes values in a convex domain “ , and hence giving an answer to a Theorem of Ziad S.Ali.in [7] .We indicate further that the new sequence
منابع مشابه
On a Multiplier of the Progressive Means and Convex Maps of the Unit Disc
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