Stud. Univ. Babe¸ s-Bolyai Math. 61(2016), No. 1, 45–52 Coefficient inequality for subclass of analytic univalent functions related to simple logistic activation functions Abiodun Tinuoye Oladipo Abstract. The author investigates the relationship between unified subclasses of analytic univalent functions and simple logistic activation function to determine the initial Taylor series coefficients alongside classical Fekete-Szeg˝ o problem. Mathematics Subject Classification (2010): 30C45, 33E99. Keywords: Analytic, univalent, sigmoid, logistic activation, Fekete-Szeg˝ o, S˘ al˘ agean operator, coefficient inequalities. 1. Introduction and preliminaries The theory of special functions are significantly important to scientist and en- gineers with mathematical calculations. Though not with any specific definition but its applications extends to physics, computer etc. In the recent time, theory of spe- cial function has been overshadowed by other fields such as real analysis, functional analysis, differential equation, algebra and topology. There are various special functions but we shall concern ourselves with one of the activation function popularly known as sigmoid function or simple logistic function. By activation function, we meant an information process inspired by the same way biological nervous system (such as brain) process information. This composed of large number of highly interconnected processing element, that is neurons, working as a unit to solve or process a specific task. It also learns by examples, can not be programmed to solve a specific task. Sigmoid function (simple logistic activation function) has a gradient descendent learning algorithm, its evaluation could be done in several ways (even by truncated series expansion). The simple logistic activation function is given as L(z)= 1 1+ e −z (1.1)