Generalized uniformly close-to-convex functions of order γ and type β

Authors : F.m. AL-OBOUDİ

Pages : 173-182

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Publication Date : 2014-04-01

Article Type : Research Paper

Abstract :In this paper, a class of analytic functions f defined on the open unit disc satisfying Re  zinsert ignore into journalissuearticles values(D n,α λ finsert ignore into journalissuearticles values(z););0 D n,α λ ginsert ignore into journalissuearticles values(z);  > β zinsert ignore into journalissuearticles values(D n,α λ finsert ignore into journalissuearticles values(z););0 D n,α λ ginsert ignore into journalissuearticles values(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