Coefficient inequalities for a new class of univalent functions

In the present article, a new class ∑ α , 0 ≤ α < 1, of analytic and univalent functions f: U → C where U is an open unit disk, satisfying the standard normalization f(0) = f′(0) - 1 = 0 is considered. Assume that f ∑ α takes the form such that A 0,0 = 0 and A 1,0 = 1. Also, we define the family Co(p), where p (0, 1), of functions f: U →C that satisfy the following conditions: (i) f ∑ α is meromorphic in U and has a simple pole at the point p. (ii) f(0) = f′(0) - 1 = 0. (iii) f maps U conformally onto a set whose complement with respect toC is convex. We call such functions concave univalent functions. We prove some coefficient estimates for functions in this class when f has the expansion The second part of the article concerns some properties of a generalized Sǎlǎgean operator for functions in ∑ α . Moreover, a result on subordination for the functions f ∑ α is given. © 2008 MAIK Nauka.