Coefficient functionals for a class of bounded turning functions related to modified sigmoid function

Abstract

The main objective of the present article is to define the class of bounded turning functions associated with modified sigmoid function. Also we investigate and determine sharp results for the estimates of four initial coefficients, Fekete-Szegö functional, the second-order Hankel determinant, Zalcman conjucture and Krushkal inequality. Furthermore, we evaluate bounds of the third and fourth-order Hankel determinants for the class and for the 2-fold and 3-fold symmetric functions.

Keywords

• analytic functions
• modified sigmoid function
• subordination
• hankel determinant
• 2-fold and 3-fold symmetric function
• zalcman conjucture
• krushkal inequality