Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2911 2022 2022 Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Iraq. Audy Audy In this work, we found sharp estimates for the Zalcman conjecture and second order Hankel determinant for the inverse function when it belongs to the class of starlike functions with respect to symmetric points, denoted by . These results are new. 2024 2024 61 65 10.54216/GJMSA.0100206 https://www.americaspg.com/articleinfo/33/show/2911