Notes on certain analytic functions

Abstract

Let A(n) be the class of functions

f(z) = a(n)z(n) + a(n+1)z(n+1) +...(n is an element of N),

which are analytic in the open unit disk U, where a(n) not equal 0. For f(z) is an element of A(n), Miller and Mocanu in 1978 showed a very interesting result for f(z). Applying the result due to Miller and Mocanu, we would like to consider some new results for such functions. Our results in this paper are generalizations for results by Nunokawa in 1992.