Volume 9 , Issue 1 , PP: 23-30, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Aqeel K. AL-khafaji 1 * , Heyam K. Alkhayyat 2 , M. Abdul-Jabbar Albayati 3
Doi: https://doi.org/10.54216/GJMSA.090102
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.
Analytic function , univalent function , -univalent functions ,   , symmetric -univalent functions , Hankel determinant , Fekete-Szegö , functional.
[1] Adegani, E. A., Hamidi, S. G., Jahangiri, J. M., & Zireh, A. Coefficient estimates for m-fold symmetric -subordinate functions. Hacettepe Journal of Mathematics and Statistics, 48(2), 365-371 .2019
[2] Akgül, A., & Campus, U. On the coefficient estimates of analytic and -univalent symmetric functions. Mathematica Aeterna, 7(3), 253-260 . 2017
[3] Al-Khafaji, A. K. On initial Coefficients Estimates for Certain New Subclasses of -Univalent Functions Defined by a Linear Comμnation. Computer Science, 15(2), 491-500 . 2020
[4] Babalola, K. O. On Hankel determinant for some classes of univalent functions. arXiv preprint arXiv: 0910.3779 (2009)
[5] Bulut, S. Coefficient estimates for a new subclass of m-fold symmetric analytic -univalent functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1401-1410 (2019)
[6] Hussain, S., Khan, S., Zaighum, M. A., & Darus, M. On certain classes of -Univalent functions related to m-fold symmetry. J. Nonlinear Sci. Appl, 11, 425-434 (2018)
[7] Hussain, S.; Khan, S.; Roqia, G.; Darus, M. Hankel Determinant for certain classes of analytic functions. J. Comput. Theoret. Nanosci. 13, 9105–9110 (2016)
[8] Janteng, A.; Abdul-Halim, S.; Darus, M. Hankel determinant for starlike and convex functions. Internat. J. Math. Anal. 1, 619–625 (2007)
[9] Koepf, W. Coefficients of symmetric functions of bounded boundary rotation. Proceedings of the American Mathematical Society, 105(2), 324-329. (1989)
[10] Kuroki, K., Hayami, T., Uyanik, N., & Owa, S. Some properties for a certain class concerned with univalent functions. Computers & Mathematics with Applications, 63(10), 1425-1432 (2012)
[11] Magesh, N., & Yamini, J. Fekete-Szegö problem and second Hankel determinant for a class of -univalent functions. Tbilisi Mathematical Journal, 11(1), 141-157 (2018)
[12] Naik, U. H., & Patil, A. B. On initial coefficient inequalities for certain new subclasses of -univalent functions. Journal of the Egyptian Mathematical Society, 25(3), 291-293 (2017)
[13] Noonan, J.W.; Thomas, D.K. On the second Hankel derminant of a really mean p-valent functions. Trans. Am. Math. Soc. 223, 337–346 (1976)
[14] Ozaki, S., & Nunokawa, M. The Schwarzian derivative and univalent functions. Proceedings of the American Mathematical Society, 392-394 (1972)
[15] Pommerenke, C. On the coefficients of close-to-convex functions. The Michigan Mathematical Journal, 9(3), 259-269 (1962)
[16] Pommerenke, C. Univalent functions. Vandenhoeck and Ruprecht. (1975)
[17] Porwal, S., & Kumar, S. New subclasses of -univalent functions defined by multiplier transformation. Studia Universitatis Babes-Bolyai, Mathematica, 65(1) (2020)
[18] Ramadan, S. F., & Darus, M. New Subclasses of Analytic And m-Fold Symmetric -Univalent Functions Defined by Differential Operator. Journal of Quality Measurement and Analysis JQMA, 15(2), 35-45 (2019)
[19] Sakar, F. M., & Güney, H. O. Faber Polynomial Coefficient Estimates for Subclasses of m-fold Symmetric -univalent Functions Defined by Fractional Derivative. Malaysian Journal of Mathematical Sciences, 11, 275-287 (2017)
[20] Singh, G.; Singh, G. On the second Hankel determinant for a new subclass of analytic functions. J. Math. Sci. Appl. 2, 1–3 (2014)
[21] Srivastava, H. M., Altınkaya, Ş., & Yalçın, S. Certain subclasses of -univalent functions associated with the Horadam polynomials. Iranian Journal of Science and Technology, Transactions A: Science, 43(4), 1873-1879. (2019)
[22] Srivastava, H. M., Gaboury, S., & Ghanim, F. Initial coefficient estimates for some subclasses of m-fold symmetric -univalent functions. Acta Mathematica Scientia, 36(3), 863-871 (2016)
[23] Srivastava, H. M., Sivasubramanian, S., & Sivakumar, R. Initial coefficient bounds for a subclass of m-fold symmetric -univalent functions. Tbilisi Mathematical Journal, 7(2) (2014)
[24] Srivastava, H.M., Mishra, A.K., Gochhayat, P. Certain subclasses of analytic and - univalent functions, Appl. Math. Lett., 23, 1188-1192 ( (2010