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Univalent functions with negative coefficients based on order of convolution consistence. (English) Zbl 1344.30013

Summary: In this paper we consider the modified Hadamard product or convolution of analytic functions with negative coefficients, combined with an Sălăgean integral operator. We discuss when it is a given class. Following idea of U. Bednarz and J. Sokól we shall determine the order of convolution consistence for certain 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
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