Advances in Pure Mathematics, 2017, 7, 641-646 http://www.scirp.org/journal/apm ISSN Online: 2160-0384 ISSN Print: 2160-0368 DOI: 10.4236/apm.2017.711038 Nov. 24, 2017 641 Advances in Pure Mathematics On a Subordination Result of a Subclass of Analytic Functions Risikat Ayodeji Bello Department of Mathematics and Statistics, College of Pure and Applied Science, Kwara State University, Malete, Nigeria Abstract In this paper, we investigate a subordination property and the coefficient in- equality for the class ( ) 1, M b , The lower bound is also provided for the real part of functions belonging to the class ( ) 1, M b . Keywords Analytic Function, Univalent Function, Hadamard Product, Subordination 1. Introduction Let A denote the class of function () f z analytic in the open unit disk { } : 1 U z z = ∈ <  and let S be the subclass of A consisting of functions univalent in U and have the form () 2 , k k k f z z az ∞ = = + ∑ (1.1) The class of convex functions of order α in U, denoted as ( ) K α is given by ( ) () () : 1 , 0 1, zf z K f S Re z U f z α α α    ′′    = ∈ + > ≤ < ∈       ′       Definition 1.1. The Hadamard product or convolution f g ∗ of the func- tion () f z and () gz , where () f z is as defined in (1.1) and the function () gz is given by () 2 , k k k gz z bz ∞ = = + ∑ is defined as: How to cite this paper: Bello, R.A. (2017) On a Subordination Result of a Subclass of Analytic Functions. Advances in Pure Mathematics, 7, 641-646. https://doi.org/10.4236/apm.2017.711038 Received: March 13, 2017 Accepted: November 21, 2017 Published: November 24, 2017 Copyright © 2017 by author and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access