International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 147842, 6 pages
http://dx.doi.org/10.1155/2012/147842
Research Article

Bounds of Hankel Determinant for a Class of Univalent Functions

Sarika Verma, Sushma Gupta, and Sukhjit Singh

Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Punjab, Longowal 148106, India

Received 31 March 2012; Revised 1 June 2012; Accepted 1 June 2012

Academic Editor: Teodor Bulboaca

Copyright © 2012 Sarika Verma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The authors study the coefficient condition for the class ℌ 𝛼 defined as the family of analytic functions 𝑓 , 𝑓 ( 0 ) = 0 and 𝑓 ′ ( 0 ) = 1 , which satisfy ℜ [ ( 1 − 𝛼 ) 𝑓 ′ ( 𝑧 ) + 𝛼 ( 1 + ( 𝑧 𝑓 ′ ′ ( 𝑧 ) ) / ( 𝑓 ′ ( 𝑧 ) ) ) ] > 𝛼 , 𝑧 ∈ 𝐸 , where 𝛼 is a real number.