On the order of convolution consistence of the analytic functions with negative coefficients
Grigore S. Sălăgean, Adela Venter
Received May 4, 2015. First published February 2, 2017.
Abstract: Making use of a modified Hadamard product, or convolution, of analytic functions with negative coefficients, combined with an integral operator, we study when a given analytic function is in a given class. Following an idea of U. Bednarz and J. Sokół, we define the order of convolution consistence of three classes of functions and determine a given analytic function for certain classes of analytic functions with negative coefficients.
Keywords: analytic function with negative coefficients; univalent function; extreme point; order of convolution consistence; starlikeness; convexity
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Affiliations: Grigore S. Sălăgean, Babes-Bolyai University, Faculty of Mathematics and Computer Science, Str. Kogalniceanu Nr. 1, 400084 Cluj-Napoca, Romania, e-mail: email@example.com; Adela Venter, Faculty of Enviromental Protection, University of Oradea, Str. Universitatii Nr. 1, 410087 Oradea, Romania, e-mail: firstname.lastname@example.org