Open problems on univalent and multivalent functions
نویسندگان
چکیده
منابع مشابه
On Univalent Harmonic Functions
Two classes of univalent harmonic functions on unit disc satisfying the conditions ∑∞ n=2(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) and ∑∞ n=2 n(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning th...
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Let F„ denote the wth coefficient region for this class of functions [S, §1.2]. Let F=Fia2, ä2, ■ • ■ , a„, a«) be a real-valued function. Write x,= (l/2)(a,+á,), y,= (l/2í)(a,-á,), F,= (l/2)(r3F/r)x, — idF/dy,). Let F satisfy the further conditions (a) F is defined in an open set O containing V„, (b) F and its derivatives F, are continuous in 0, (c) |grad F\ = ( E?-a | F,\ 2)1/2>0 in 0. Let/(z...
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We consider the class of analytic functions B(α) to investigate some properties for this class. The angular estimates of functions in the class B(α) are obtained. Finally, we derive some interesting conditions for the class of strongly starlike and strongly convex of order α in the open unit disk. 2000 Mathematics Subject Classification. Primary 30C45.
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Let * (p,α) be the class of functions f (z) which are analytic and p-valently starlike of order α in the open unit disk E. The object of the present paper is to derive an interesting condition for f (z) to be in the class * (p,α). This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution , and reproduction in any ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1968
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1968-12045-2