A new class of multivalent analytic functions defined by the Hadamard product

Abstract

Abstract. The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for classes of functions with two fixed points. Some remarks depicting consequences of the main results are also mentioned. IntroductionLet A denote the class of functions which are analytic in U = U(1), where U(r) = {z ∈ C: |z| < r}.and let A (p, k) (p, k ∈ N = {1, 2, 3...} , p < k) denote the class of functions f ∈ A of the formOne can obtain interesting results by applying normalization of the formwhere ρ is a fixed point of the unit disk U. In particular, for p = 1 we obtain Montel's normalization (cf.[8]). We see that for ρ = 0 the normalization (3) is the classical normalization.1991 Mathematics Subject Classification: 30C45.