Abstract
In this article, we define the class of bounded turning functions connected with three leaf function to investigate results for the estimates of four initial coefficients, Fekete-Szego functional, the second-order Hankel determinant and Zalcman conjecture and these results are shown to be sharp. Furthermore, we estimate the bounds of the third-order Hankel determinants for this class and for its 2-fold and 3-fold symmetric functions. Finally we evaluate the sharp Krushkal inequality for the functions in this class.