- Hacettepe Journal of Mathematics and Statistics
- Vol: 43 Issue: 2
- Generalized uniformly close-to-convex functions of order γ and type β
Generalized uniformly close-to-convex functions of order γ and type β
Authors : F. M. Al-oboudi
Pages : 173-182
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Publication Date : 2014-04-01
Article Type : Research
Abstract :In this paper, a class of analytic functions f defined on the open unit disc satisfying Re z(D n,α λ f(z))0 D n,α λ g(z) > β z(D n,α λ f(z))0 D n,α λ g(z) − 1 + γ, is studied, where β ≥ 0, −1 ≤ γ < 1, β + γ ≥ 0. and g is a certain analytic function associated with conic domains. Among other results, inclusion relations and the coefficients bound are studied. Various known special cases of these results are pointed out. A subclass of uniformly quasi-convex functions is also studied.Keywords : Univalent functions, uniformly close-to-convex, uniformly quasiconvex, fractional differential operator