aspg-33-2911-1792223535 20261017075215 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2024 10 2 Audy Hatim Saheb Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Iraq. 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 style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi'> style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-IQ;font-style:italic; mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font: minor-fareast;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-IQ'>S style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font: minor-fareast;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-IQ'>s style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font: minor-fareast;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-IQ'>* . These results are new. 2024 61 65 2911 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.0100206 https://americaspg.com/journal/33/article/2911 https://americaspg.com/storage/41719250904.pdf