Coefficient Estimates for Certain Classes of Bi-Univalent Functions. (29th August 2013)

• Record Type: Journal Article
• Authors: Jahangiri, Jay M.; Hamidi, Samaneh G.
• Other Names: Begehr Heinrich Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2013(2013)
• Publication Date: 2013-08-29
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2013/190560
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : A function analytic in the open unit disk 𝔻 is said to be bi-univalent in 𝔻 if both the function and its inverse map are univalent there. The bi-univalency condition imposed on the functions analytic in 𝔻 makes the behavior of their coefficients unpredictable. Not much is known about the behavior of the higher order coefficients of classes of bi-univalent functions. We use Faber polynomial expansions of bi-univalent functions to obtain estimates for their general coefficients subject to certain gap series as well as providing bounds for early coefficients of such functions.