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On the order of convolution consistence of the analytic functions with negative coefficients. (English) Zbl 1463.30078

Summary: 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 [Stud. Univ. Babeş-Bolyai, Math. 55, No. 3, 41–50 (2010; Zbl 1240.30037)], 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.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable

Citations:

Zbl 1240.30037
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