On a sufficient condition for strongly starlikeness
نویسندگان
چکیده
منابع مشابه
Some 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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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...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2013
ISSN: 1029-242X
DOI: 10.1186/1029-242x-2013-383