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.
