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A subclass of harmonic univalent functions with negative coefficients

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Karpuzoǧulları, Sibel Yalçın
Öztürk, Metin
Yamankaradeniz, Mümin

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Elsevier

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Complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f h + (g) over bar, where h and g are analytic in U. In this paper, consider the class HP(beta), (0 less than or equal to beta < 1) consisting of harmonic and univalent functions f = h + (g) over bar for which Re{ h'(z) + g'(z)} > beta. We give sufficient coefficient conditions for normalized harmonic functions in the class HP(beta). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.

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Mathematics, Harmonic functions, Extreme points, Distortion bounds, Computation theory, Functions, Set theory, Distortion bounds, Harmonic analysis

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Karpuzoǧulları, S. Y. vd. (2003). “A subclass of harmonic univalent functions with negative coefficients”. Applied Mathematics and Computation, 142(2-3), 469-476.

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