Sufficient conditions for multivalent starlikeness
نویسندگان
چکیده
منابع مشابه
Sufficient conditions for univalence and starlikeness
It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|
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Let A,B,D,E ∈ [−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0) = 1. Conditions on A, B, D, and E are determined so that 1 + βzp′(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1 + β(zp′(z)/p(z)) and 1 + β(zp′(z)/p2(z)). These results are then applied to obtain s...
متن کاملOn Certain Sufficient Conditions for Starlikeness
We consider certain properties of f(z)f ′′(z)/f ′2(z) as a sufficient condition for starlikeness.
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The object of the present paper is to derive certain sufficient conditions for univalence, p-valently starlikeness and p-valently close-to-convexity of analytic functions in the unit disk. Our results extend and improve some results due to Owa [3], Frasin and Darus [2] and Chen [1].
متن کاملSome Sufficient Conditions for Strongly Starlikeness
We consider strongly starlikeness of order α of functions f(z)= z+an+1zn+1 +··· which are analytic in the unit disc and satisfy the condition of the form ∣∣∣∣f ′(z) ( z f(z) )1+μ −1 ∣∣∣∣< λ, 0< μ < 1, 0< λ< 1.
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1995
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-62-1-75-78