Fekete-Szegö inequality for generalized subclasses of univalent functions

Abstract

Abstract. Let P ϕ (n,b,λ ) denote the class of normalized univalent functions f (z) = z + a 2 z 2 + ..., which are defined in the unit disk Δ and satisfying 1, where ϕ(z) is the function with positive real part, D n f denotes the sȃlȃgean operator, n 0 , 0 λ 1 , b ∈ C . In this paper, for the class P ϕ (n,b,λ ) , the Fekete-Szegö inequalities are completely solved. A more general class K (β ,n,λ ,g(z)) related P ϕ (n,b,λ ) is also considered with same subject, which extends the earlier corresponding results for the class of strongly close-to-convex functions of order β .Mathematics subject classification (2010): 30C45, 30C50.