Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function

In this article we define a class of starlike functions with respect to symmetric points in the domain of sine function. Also, we investigate coefficients bounds and upper bounds for the third order Hankel determinant for this defined class. We also evaluate the Zalcman functional \(|a₃²-a₅|\). Specializing the parameters, we improve Zalcman functional for the class of starlike functions.