doi: 10.2478/umcsmath-2014-0007 ANNALES UNIVERSITATIS MARIAE CURIE-SKŁODOWSKA LUBLIN – POLONIA VOL. LXVIII, NO. 1, 2014 SECTIO A 59–66 E. A. OYEKAN and T. O. OPOOLA On a subordination result for analytic functions defined by convolution Abstract. In this paper we discuss some subordination results for a subclass of functions analytic in the unit disk U . 1. Introduction. Let A be the class of functions f (z ) analytic in the unit disk U = {z : |z | < 1} and normalized by (1.1) f (z )= z + ∞  n=2 a n z n . We denote by K(α) the class of convex functions of order α, i.e., K(α)=  f ∈ A : Re  1+ zf ′′ (z ) f ′ (z )  > α, z ∈ U  . Definition 1 (Hadamard product or convolution). Given two functions f (z ) and g(z ), where f (z ) is defined in (1.1) and g(z ) is given by g(z )= z + ∞  n=2 b n z n , 2000 Mathematics Subject Classification. 30C45, 30C80. Key words and phrases. Subordination, analytic functions, Hadamard product (convolution). brought to you by CORE View metadata, citation and similar papers at core.ac.uk