In this paper, we define a general class of α-convex functions,
denoted by MLβ,α(q), with respect to a convex domain
D (q(z) ∈ Hu(U), q(0) = 1 , q(U) = D) contained in the right half
plane by using the linear operator D
β
λ
defined by
D
β
λ
: A → A ,
D
β
λ
f(z) = z +
X∞
j=2
(1 + (j − 1)λ)
β
ajz
j
,
where β, λ ∈ R, β ≥ 0, λ ≥ 0 and f(z) = z+
X∞
j=2
ajz
j
. Regarding the
class MLβ,α(q), we give a inclusion theorem and a transforming
theorem, from which we may obtain many particular results.
The aim of this paper is to give the radius of starlikeness of the certain classes of Open image in new window-valent functions defined by multiplier transformations. The results are obtained by using techniques of Robertson (1953,1963) which was used by Bernardi (1970), Libera (1971), Livingstone (1966), and Goel (1972).
