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

Year 2014, Volume: 43 Issue: 2, 173 - 182, 01.04.2014

F.m. Al-oboudi

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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