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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2015 | 113 | 3 | 295-304

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

EN

### Abstrakty

EN
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.

295-304

wydano
2015

### Twórcy

autor
• Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam, India
autor
• Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam, India
autor
• Institute of Mathematics, University of Rzeszów, Rzeszów, Poland
autor
• Department of Mathematics Education, Dongguk University, Gyeongju, Korea