Let M(n+p-1) (alpha) denote the class of functions of the form f(z) =
1/z(p) + a0/z(p-1) + ... + a(k+p-1) z(k) + ..., p is-an-element-of N =
{1,2,3, ...}, that are regular in the annulus D = {z: 0 < absolute va
lue of z < 1} and satisfy Re{z(D(n+p-1)f(z))'/D(n+p-1)f(z)} < -alpha f
or 0 less-than-or-equal-to alpha < p and absolute value of z < 1, wher
e D(n+p-1)f(z) = 1/z(p) (z(n+2p-1)f(z)/(n+p-1)!)(n+p-1). We prove that
M(n+p)(alpha) subset-of M(n+p-1)(alpha), where n is any integer great
er than -p. We also consider some integrals of functions in the class
M(n+p-1)(alpha).