New Subclass of Close-to-convex Functions Associated with the Vertical Strip Domains

Author(s):

Hesam Mahzoon* , Janusz Sokól

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

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.<betaquad</betaquad

Keywords:

Univalent , Close-to-convex , Differential subordination , Coefficient estimates , Fekete-Szegö problem

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:18 Issue: 2, Nov 2023
Pages:
199 to 210
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