NEIGHBORHOODS OF CERTAIN ANALYTIC-FUNCTIONS

Two subclasses P(n)(alpha) and Q(n)(alpha) of certain analytic functio ns in the open unit disk U are introduced. For p(z) is-an-element-of P (n)(alpha) and delta(n) greater-than-or-equal-to 0, the delta(n)-neigh borhood N(delta)n (p(z)) of p(z) is defined. For P(n)(alpha), Q(n)(alp ha), and N(delta)n (p(z)), we prove that if p(z) is-an-element-of Q(n) (alpha), then N(1-alpha)delta(n)(P(z)) subset-of P(n)(alpha).