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On the order of convolution consistence of the analytic functions with negative coefficients

Grigore S. Sălăgean, Adela Venter (2017)

Mathematica Bohemica

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.

On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

Agnieszka Sibelska (2010)

Annales UMCS, Mathematica

The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ. In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998-2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazińska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri [6],...

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