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

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

References

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