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A note on Briot-Bouquet-Bernoulli dierential subordination

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Stanis lawa Kanas, Joanna Kowalczyk

A note on Briot-Bouquet-Bernoulli dierential subordination

Comment.Math.Univ.Carolinae 46,2 (2005) 339-347.

Abstract: Let p, q be analytic functions in the unit disk U. For α ∈ [0,1) the authors consider the differential subordination and the differential equation of the Briot-Bouquet type:

p1−α(z) + zp0(z)

δpα(z) +λp(z)≺h(z), z∈ U, q1−α(z) + nzq0(z)

δqα(z) +λq(z) =h(z), z∈ U,

with p(0) = q(0) = h(0) = 1. The aim of the paper is to find the dominant and the best dominant of the above subordination. In addition, the authors give some particular cases of the main result obtained for appropriate choices of functionsh.

Keywords: differential subordinations, Briot-Bouquet-Bernoulli differential sub- ordination

AMS Subject Classification: 34A25, 30C35, 30C45

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