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Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions

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Sivasubramanian S., Sivakumar R., Kanas S., Kim S.-A.

Annales Polonici Mathematici

2015

tom 113

nr 3

295-304

Let σ denote the class of bi-univalent functions f, that is, both f(z) = z + a₂z² + ⋯ and its inverse $f^{-1}$ are analytic and univalent on the unit disk. We consider the classes of strongly bi-close-to-convex functions of order α and of bi-close-to-convex functions of order β, which turn out to be subclasses of σ. We obtain upper bounds for |a₂| and |a₃| for those classes. Moreover, we verify Brannan and Clunie's conjecture |a₂| ≤ √2 for some of our classes. In addition, we obtain the Fekete-Szegö relation for these classes.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Kanas S.

1 Kim S.-A.

1 Sivakumar R.

1 Sivasubramanian S.

1 2015

Wyniki wyszukiwania

Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions