Coefficient Inequality for Certain Subclasses of Analytic Functions

New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 217-228

D. Vamshee Krishna

Department of Engineering Mathematics,

Gitam Institute of Technology,

Rushikonda,

GITAM University,

Visakhapatnam-530 045,

India.

T. Ramreddy

Department of Mathematics,

Kakatiya University,

Vidyaranyapuri- 506 009,

Warangal Dt.,

India.

Abstract The objective of this paper is to introduce certain subclasses of analytic functions and seek an upper bound to the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for the function f belonging to these classes, using Toeplitz determinants.

Keywords Analytic function, upper bound, second Hankel determinant, positive real function, Toeplitz determinants.

Classification (MSC2000) 30C45; 30C50.