Let σ denote the class of bi-univalent functions f, that is, both f(z) = z + a₂z² + ⋯ and its inverse 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-3-6,
author = {S. Sivasubramanian and R. Sivakumar and S. Kanas and Seong-A Kim},
title = {Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {295-304},
zbl = {1332.30029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-3-6}
}
S. Sivasubramanian; R. Sivakumar; S. Kanas; Seong-A Kim. Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions. Annales Polonici Mathematici, Tome 113 (2015) pp. 295-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-3-6/