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

Sălăgean, Grigore S.; Venter, Adela

Math. Bohem. 142, No. 4, 381-386 (2017).

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

Keywords:

analytic function with negative coefficients; univalent function; extreme point; order of convolution consistence; starlikeness; convexity

Citations:

Zbl 1240.30037