Abstract
The object of the present paper is to introduce new classes of meromorphic functions with varying argument of coefficients defined by means of the Hadamard product (or convolution). Several properties like the coefficients bounds, growth and distortion theorems, radii of starlikeness and convexity, and partial sums are investigated. Some consequences of the main results for well‐known classes of meromorphic functions are also pointed out.
Highlights
Let M denote the class of functions which are analytic in D D 1, whereD r {z ∈ C : 0 < |z| < r}, 1.1 with a simple pole in the point z 0
By M, we denote the class of functions f ∈ M of the form fz anzn n1 z∈D
By Tεη η ∈ R, ε ∈ {0, 1}, we denote the class of functions f ∈ M of the form 1.2 for which arg an επ − n 1 η n ∈ N : {1, 2, 3, . . .}
Summary
D r {z ∈ C : 0 < |z| < r}, 1.1 with a simple pole in the point z 0. By M, we denote the class of functions f ∈ M of the form fz 1 z. By Tεη η ∈ R, ε ∈ {0, 1} , we denote the class of functions f ∈ M of the form 1.2 for which arg an επ − n 1 η n ∈ N : {1, 2, 3, . For η 0, we obtain the classes T00 and T10 of functions with positive coefficients and negative coefficients, respectively. It is easy to show that for a function f ∈ T0η, the condition 1.6 is equivalent to the following: zf z fz 1
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