aspg-33-2263-1792223319 20261017074839 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2023 9 1 Aqeel K. AL-khafaji Faculty of Education for Pure Sciences, Mathematics department, Babylon University, Iraq Heyam K. Alkhayyat Faculty of Computer Science and mathematics, Mathematics departmen, University of Kufa, Iraq M. Abdul-Jabbar Albayati Faculty of Administration and Economics, Economics department, University of Misan, Iraq This paper introduces and investigate a new subclasses of the class 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:Calibri;mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; font-style:italic;mso-bidi-font-style:normal'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-fareast-font-family: Calibri;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="roman"/>Σ style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-fareast-font-family: Calibri;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="roman"/>μ of analytic functions that both style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="i"/>g mso-fareast-font-family:Calibri;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'>and style='mso-bidi-font-style:normal'> 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:Calibri;mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="i"/>g normal'> mso-fareast-font-family:Calibri;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'> m:val="i"/>-1 are style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-fareast-font-family: Calibri;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="roman"/>μ -fold style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-fareast-font-family: Calibri;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="roman"/> symmetric style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'>bi -univalent functions in the open unit disk lang=AR-SA dir=RTL style='font-size:10.0pt;font-family:"Times New Roman",serif; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-bidi-theme-font:major-bidi;mso-ansi-font-style:italic'>Ω and get the estimates of the initial coefficients m:val="|"/> 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; font-style:italic;mso-bidi-font-style:normal'> 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;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> font-family:"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'>α style='mso-bidi-font-style:normal'> font-family:"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'>t+1 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'>, 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;font-style:italic;mso-bidi-font-style:normal'> 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;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> font-family:"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'>α style='mso-bidi-font-style:normal'> font-family:"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'>2t+1 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'> a 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'> m:val="roman"/>nd normal'> 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;font-style:italic;mso-bidi-font-style:normal'> 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;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> font-family:"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'>α style='mso-bidi-font-style:normal'> font-family:"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'>3t+1 for functions in each of these new subclasses. After this, the work will be discussing the Hankel determinant and a Fekete-Szegö functional. 2023 23 30 2263 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.090102 https://americaspg.com/journal/33/article/2263 https://americaspg.com/storage/61701345271.pdf