CERTAIN DIFFERENTIAL-OPERATORS FOR MEROMORPHICALLY P-VALENT CONVEX-FUNCTIONS

Let J(n)(alpha) be the class of functions of the form [GRAPHICS] which are regular in the punctured disk E = {z:0 < \z\ < 1} and satisfying Re{(D(n+1)f(z))'/(D(n)f(z))'-(p+1)} < -p(n+alpha)/(n+1) n is-an-element-of N0 = {0,1,2,...},\z\ < 1,0 less-than-or-equal-to alpha < 1), where [GRAPHICS] It is proved that J(n+1)(alpha) subset-of J(n)(alpha). Since J0(alpha) is the class of meromorphically p-valent convex functions of order alpha, all functions in J(n)(alpha) are p-valent convex. Further properties preserving integrals are considered.