An upper bound to the second Hankel functional for the class of gamma-starlike functions

Vamshee Krishna, D‎. ‎; ‎Ramreddy, T.

An upper bound to the second Hankel functional for the class of gamma-starlike functions

Document Type : Research Paper

Authors

D‎. ‎ Vamshee Krishna ¹
T. ‎Ramreddy ²

¹ Department of Mathematics‎, ‎GIT‎, ‎GITAM University‎, ‎Visakh-apatnam-530 045‎, ‎Andhra Pradesh‎, ‎India

² Department of Mathematics, Kakatiya University‎, Warangal- 506009, Telangana State, ‎India.

Abstract

‎The objective of this paper is to obtain an upper bound to the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$‎ ‎for the function $f$‎, ‎belonging to the class of Gamma-starlike functions‎, ‎using Toeplitz determinants‎. ‎The result presented here include‎ ‎two known results as their special cases‎.

Keywords