  There are many results for sufficient conditions of functions f(z) which are
analytic in the open unit disc U to be starlike and convex in U. The object of
the present paper is to derive some interesting sufficient conditions for f(z)
to be starlike of order \alpha\ and convex of order \alpha\ in U concerned with
Jack's lemma. Some examples for our results are also considered with the help
of Mathematica 5.2.
