Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2263 2022 2022 Faculty of Education for Pure Sciences, Mathematics department, Babylon University, Iraq Aqeel K. AL .. Faculty of Computer Science and mathematics, Mathematics departmen, University of Kufa, Iraq Heyam K. Alkhayyat Faculty of Administration and Economics, Economics department, University of Misan, Iraq M. Abdul-Jabbar Albayati This paper introduces and investigate a new subclasses of the class  of analytic functions that both are -fold symmetric -univalent functions in the open unit disk  and get the estimates of the initial coefficients  for functions in each of these new subclasses. After this, the work will be discussing the Hankel determinant and a Fekete-Szegö functional. 2023 2023 23 30 10.54216/GJMSA.090102 https://www.americaspg.com/articleinfo/33/show/2263