ZALCMAN CONJECTURE AND HANKEL DETERMINANT OF ORDER THREE FOR STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH SHELL-LIKE CURVES

Abstract

The aim of this article is to estimate an upper bound of |𝐻_3(1)|, the Zalcman coefficient functional for 𝑛 = 3 and 𝑛 = 4, and also to investigate the fifth, sixth, seventh coefficients of starlike and convex functions associated with shell-like curves. Similar type of outcomes are estimated for the functions 𝑓^(−1) and 𝑧/𝑓(𝑧).

Keywords

• analytic function
• function with positive real part
• starlike function
• subordination
• zalcman conjecture
• shell-like curve
• hankel determinant