Maclaurin Coefficients Estimates for New classes of m-Fold Symmetric Bi-Univalent Functions

Authors

  • Elaf Ibrahim Badiwi Department of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf- Iraq
  • Waggas Galib Atshan Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah –Iraq
  • Ameera N. Alkiffai Department of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf- Iraq

DOI:

https://doi.org/10.29304/jqcsm.2024.16.21536

Keywords:

Analytic function, Bi-univalent functions, Coefficient estimates

Abstract

The purpose of this study is to establish new subclasses within the function class , which consists of analytic as well as -fold symmetric bi-univalent functions expressed within the open unit disk . Additionally, for functions belonging to each of the newly established subclasses, this paper establishes estimates with regards to the Taylor-Maclaurin coefficients given by  as well as . Moreover, we take into consideration of specific as well as existing special cases for our respective findings.

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References

E. A. Adegani, S. Bulut and A. A. Zireh, Coefficient estimates for a subclass of analytic bi-univalent functions, Bull. Korean Math. Soc., 55(2)(2018), 405-413.

S. Altinkaya and S. Yalçin, Coefficient bounds for certain subclasses of m-fold symmetric bi-univalent functions, Journal of Mathematics, Art. ID 241683, (2015), 1-5.

S. Altinkaya and S. Yalçin, On some subclasses of m-fold symmetric bi-univalent functions, Commun. Fac. Sci. Univ. Ank. Series A1, 67(1)(2018), 29-36.

A. Amourah, A. Alamoush, and M. Al-Kaseasbeh, Gegenbauer polynomials and bi univalent functions, Palestine Journal of Mathematics, 10(2) (2021), 625-632.

W. G. Atshan and E. I. Badawi, On sandwich theorems for certain univalent functions defined by a new operator, Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(2)(2019) ,72–80.

E. I. Badiwi, W. G. Atshan, A. N. Alkiffai and A. A. Lupas, Certain results on subclasses of analytic and bi-univalent functions associated with coefficient estimates and quasi-subordination, Symmetry, 15(12) (2023), 2208, 1-12.

D. A. Brannan and T. S. Taha, On Some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math., 31(2)(1986), 70–77.

S. Bulut, Coe_cient estimates for general subclasses of m-fold symmetric analytic bi univalent functions, Turkish J. Math., 40 (2016), 1386-1397.

P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.

S. S. Eker, Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions, Turk. J. Math., 40(2016), 641-646.

B. A. Frasin and M. K. Aouf, Coe_cient bounds for certain classes of bi-univalent functions, Hacettepe Journal of Mathematics and Statistics, 43(3) (2014), 383–389.

S. K. Gebur and W.G. Atshan, Second Hankel determinant and Feket-Szego problem for a new class of bi-univalent functions involving Eulerpolynomials, Symmetry,16(5)(2024),530,1-18

S. P. Goyal and P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc., 20 (2012), 179-182.

B. Khan, H. M. Srivastava, M. Tahir, M. Darus, Q. Z. Ahmad and N. Khan, Applications of a certain q-integral operator to the subclasses of analytic and bi-univalent functions, AIMS Mathematics, 6 (2021), 1024-1039.

W. Koepf, Coefficients of symmetric functions of bounded boundary rotations, Proc. Amer. Math. Soc., 105(1989), 324-329.

T. R. K. Kumar, S. Karthikeyan, S. Vijayakumar and G. Ganapathy, Initial coefficient estimates for certain subclasses of m-fold symmetric bi-univalent functions, Advances in Dynamical Systems and Applications, 16( 2) (2021), 789-800.

X. F. Li and A. P. Wang, Two new subclasses of bi-univalent functions, Int. Math. Forum, 7(2)(2012), 1495-1504.

N. Magesh and J. Yamini, Fekete-Szego problem and second Hankel determinant for a class of bi-univalent functions, Tbilisi Math. J., 11(1)(2018), 141-157.

T. G. Shaba and A. K. Wanas, Initial coefficient estimates for a certain subclasses of m-fold symmetric bi-univalent functions involving ϕ-pseudo-starlike functions defined by Mittag-Leffler function, Konuralp Journal of Mathematics, 10(1)(2022), 59-68.

Q.A. Shakir, W.G. Atshan, On third Hankel determinant for certain subclass of bi-univalent functions, Symmetry, 16(2) (2024), 239, 1-10.

H. M. Srivastava and D. Bansal, Coefficient estimates for a subclass of analytic and bi-univalent functions, J. Egyptian Math. Soc., 23(2015), 242–246.

H. M. Srivastava, S. Bulut, M. Caglar and N. Yagmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27(5)(2013), 831–842.

H. M. Srivastava, S. S. Eker and R. M. Ali, Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29(2015), 1839–1845.

H. M. Srivastava, S. Gaboury and F. Ghanim, Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed., 36(2016), 863-871.

H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), 1188–1192.

H. M. Srivastava, S. Sivasubramanian and R. Sivakumar, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J., 7(2)(2014), 1-10.

H. Tang, H. M. Srivastava, S. Sivasubramanian and P. Gurusamy, The Fekete-Szego ̈ functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Inequal., 10(2016), 1063-1092.

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Published

2024-06-30

How to Cite

Ibrahim Badiwi, E., Galib Atshan, W., & N. Alkiffai, A. (2024). Maclaurin Coefficients Estimates for New classes of m-Fold Symmetric Bi-Univalent Functions. Journal of Al-Qadisiyah for Computer Science and Mathematics, 16(2), Math. 19–28. https://doi.org/10.29304/jqcsm.2024.16.21536

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Math Articles

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