Abstract
Let Q(alpha) be the class of functions of the form
f (z) = a-1/z + Sigma(infinity)(k=0) a(k)z(k) (a-1 not equal 0)
which are regular in the punctured disc U* = {z : 0 < vertical bar z vertical bar < 1} and satisfying
Re {(Dn+1 f(z))'/(D-n f(z))' -2} < -alpha, 0 <= alpha < 1, vertical bar z vertical bar < 1,
and n is an element of N-0 = {0,1,2, ...}, where
D-n f(z) = a-1/z + Sigma(infinity )(k=2)k(n) a(k-2)z(k-2).
It is proved that Q(n)(+1) (alpha) subset of Q(n) (alpha). Since Q(0) (alpha) is the class of meromorphically convex functions of order alpha(0 <= alpha < 1) the members of Q(n) (alpha) are meromorfically convex . Further property preserving integrals are considered.