منابع مشابه
Coefficient estimates for Ruscheweyh derivatives
are classes of starlike and strongly starlike functions of order β (0 < β ≤ 1), respectively. Note that S∗(β)⊂ S∗ for 0< β< 1 and S∗(1)= S∗ [5]. Kanas [2] introduced the subclass R̄δ(β) of function f ∈ S as the following. Definition 1.1. For δ ≥ 0, β ∈ (0,1], a function f normalized by (1.1) belongs to R̄δ(β) if, for z ∈D−{0} and Dδf(z)≠ 0, the following holds: ∣∣∣arg z ( Dδf(z) )′ Dδf(z) ∣∣∣≤ βπ...
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In a recent paper, V. V. Andrievskii and St. Ruscheweyh proved the existence of a universal real constant c > 0, such that for any conformal map f in the unit disk D and any n 2c, there exists a univalent polynomial pn in D of degree n with f(0) = pn(0) and f(nD) pn(D) f(D); where n := 1 ? c n : The numbers n are related to the quality of polynomial approximation of conformal maps. In this note...
متن کاملUnivalent Functions Defined by Ruscheweyh Derivatives
We study some radii problems concerning the integral operator z F(z)y+l uY-I f(u) du zy o for certain classes, namely K and M (a), of univalent functions defined by Ruscheweyh n n derivatives. Infact, we obtain the converse of Ruscheweyh’s result and improve a result of Goel and Sohi for complex by a different technique. The results are sharp.
متن کاملOn a conjecture of Danikas and Ruscheweyh
We construct a holomorphic function f in the unit disc, whose derivative belongs to the Hardy class H1 , and the image of the unit circle under z 7→ ∫ z 1 f ′(ζ) dζ ζ is a simple curve, but f is not univalent.
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ژورنال
عنوان ژورنال: Computational Methods and Function Theory
سال: 2019
ISSN: 1617-9447,2195-3724
DOI: 10.1007/s40315-019-00292-x