دوره 18، شماره 2 - ( 7-1402 )
جلد 18 شماره 2 صفحات 210-199 |
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Mahzoon H, Sokól J. New Subclass of Close-to-convex Functions Associated with the Vertical Strip Domains. IJMSI 2023; 18 (2) :199-210
URL: http://ijmsi.ir/article-1-1618-fa.html
URL: http://ijmsi.ir/article-1-1618-fa.html
New Subclass of Close-to-convex Functions Associated with the Vertical Strip Domains. مجله علوم ریاضی و انفورماتیک. 1402; 18 (2) :199-210
چکیده:
In the present paper, we introduce the class Βθ(α,β) consisting of functions f, analytic in the unit disc ∆, normalized by the condition f(0)=0=f'(0)-1 and satisfying the following two-sided inequality
α< Re{f'(z)+(1+eiθ)/2 zf''(z)}<β (z∈∆),
where θ∊(-π,π], 0<α<1 and β>1. Integral representation, differential subordination results, coefficient estimates and Fekete-Szegö coefficient functional associated with the k-th (k≥1) root transform [f(zk)]1/k for functions in the class Βθ(α,β), are determined.
α< Re{f'(z)+(1+eiθ)/2 zf''(z)}<β (z∈∆),
where θ∊(-π,π], 0<α<1 and β>1. Integral representation, differential subordination results, coefficient estimates and Fekete-Szegö coefficient functional associated with the k-th (k≥1) root transform [f(zk)]1/k for functions in the class Βθ(α,β), are determined.
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