A Survey on Cauchy–Bunyakovsky–Schwarz Inequality for Power Series Alawiah Ibrahim and Silvestru Sever Dragomir Dedicated to Professor Hari M. Srivastava Abstract In this paper, we present a survey of some recent results for the celebrated Cauchy–Bunyakovsky–Schwarz inequality for functions defined by power series with nonnegative coefficients. Particular examples for fundamental functions of interest are presented. Applications for some special functions are given as well. 1 Introduction The Cauchy–Bunyakovsky–Schwarz inequality, or for short the CBS inequality, is also known in the literature as the Cauchy’s, the Schwarz’s, or the Cauchy– Schwarz’s inequality. It plays an important role in different branches of modern mathematics such as Hilbert space theory, probability and statistics, classical real and complex analysis, numerical analysis, qualitative theory of differential equations and their applications. It is well known that the classical CBS inequality has been generalized, refined and applied by a remarkably large number of researchers for different and various motivations. For the detail, see particularly the survey paper [9], the relevant A. Ibrahim () School of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia e-mail: alawiah.ibrahim@live.vu.edu.au S.S. Dragomir School of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia School of Computational and Applied Mathematics, University of The Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa e-mail: sever.dragomir@vu.edu.au G.V. Milovanovi´ c and M.Th. Rassias (eds.), Analytic Number Theory, Approximation Theory, and Special Functions, DOI 10.1007/978-1-4939-0258-3__10, © Springer Science+Business Media New York 2014 247