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

• Autorzy: S. Sivasubramanian , R. Sivakumar , S. Kanas , Seong-A Kim
• Języki publikacji: 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.

Kategorie tematyczne

• 30C50: Coefficient problems for univalent and multivalent functions
• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C80: Maximum principle; Schwarz's lemma, Lindel\"of principle, analogues and generalizations; subordination

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 113
• Numer: 3
• Strony: 295-304

Daty

wydano

2015

Twórcy

autor

S. Sivasubramanian

• Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam, India

autor

R. Sivakumar

• Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam, India

autor

S. Kanas

• Institute of Mathematics, University of Rzeszów, Rzeszów, Poland

autor

Seong-A Kim

• Department of Mathematics Education, Dongguk University, Gyeongju, Korea

Identyfikatory

DOI

10.4064/ap113-3-6