Theoretical Mathematics & Applications, vol.6, no.4, 2016, 71-74 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2016 On a new Differential Operator Deborah Olufunmilayo Makinde 1 Abstract In this paper, we give a new differential operator for the class of analytic functions of the form: f (z )= z + ∞  n=2 a n z n . and we obtained a univalent condition for the harmonic function defined by the said differential operator as well as its coefficient bounds. Mathematics Subject Classification: 30C45 Keywords: New differential operator; harmonic function; univalent; coeffi- cient bound. 1 Introduction Let A denote the class of all analytic functions f (z ) defined in the open unit disk U = {z ∈ C : |z | < 1} and of the form: f (z )= z + ∞  n=2 a n z n (1) 1 Obafemi Awolowo University, Ile-Ife, 220005, Nigeria. E-mail: funmideb@yahoo.com, dmakinde@oauife.edu.ng, Article Info: Received : April 13, 2016. Revised : May 21, 2016. Published online : October 30, 2016.