COEFFICIENT INEQUALITY FOR MULTIVALENT BOUNDED TURNING FUNCTIONS OF ORDER α

Abstract

The objective of this paper is to obtain the sharp upper bound to the H_2(p + 1), second Hankel determinant for p-valent (multivalent) analytic bounded turning functions (also called functions whose derivatives have positive real parts) of order α (0 ≤ α < 1), using Toeplitz determinants. The result presented here includes three known results as their special cases.

Keywords

• bounded turning func- tion
• upper bound
• Hankel determinant
• positive real function
• Toeplitz determinants
• p-valent analytic function
• bounded turning function
• Toeplitz determinants