Starlikeness and convexity for analytic functions concerned with Jack's lemma

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.