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

S. Sivasubramanian, et al. "Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions." Annales Polonici Mathematici 113.3 (2015): 295-304. <http://eudml.org/doc/280248>.

@article{S2015,
abstract = {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.},
author = {S. Sivasubramanian, R. Sivakumar, S. Kanas, Seong-A Kim},
journal = {Annales Polonici Mathematici},
keywords = {star-like functions; convex functions; coefficient estimates},
language = {eng},
number = {3},
pages = {295-304},
title = {Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions},
url = {http://eudml.org/doc/280248},
volume = {113},
year = {2015},
}

TY - JOUR
AU - S. Sivasubramanian
AU - R. Sivakumar
AU - S. Kanas
AU - Seong-A Kim
TI - Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions
JO - Annales Polonici Mathematici
PY - 2015
VL - 113
IS - 3
SP - 295
EP - 304
AB - 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.
LA - eng
KW - star-like functions; convex functions; coefficient estimates
UR - http://eudml.org/doc/280248
ER -