Coefficients Estimates for Certain New Subclasses of Analytic Bi-Univalent Functions

Authors

  • Zainab Sadiq Jafar Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
  • Waggas Galib Atshan Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniya, Iraq

DOI:

https://doi.org/10.29304/jqcsm.2024.16.21562

Keywords:

Analytic function, Quasi- subordination

Abstract

This study introduces two new subclasses  and  of the function class  These subclasses are defined in the open unit disc and consist of analytic bi-univalent functions. Moreover, in these newly created subclasses, we get approximations for the  coefficients  and  in the functions. Additional findings have been acquired.

Downloads

Download data is not yet available.

References

W. G. Atshan and N. A. Jiben, Coefficients bounds for a general subclasses of m-fold symmetric bi-univalent functions, J. Al-Qadisiyah comput. Sci. Math., 9(2) (2017), 33-39.

S. A. Al-Ammeedee, W. G. Atshan and F. A. Al-Maamori, Coefficients estimates of bi-univalent functions defined by new subclasses functions, J. Phys.: Conf.Ser. 1530(2020), 012105.

W. G. Atshan, E. I. Badawi, Results on coefficients estimates for subclasses of analytic and bi-univalent functions, J. Phys. Conf. Ser., (2019), 1294, 032025, 1-9.

W. G. Atshan, I. A. R. Rahman, A. A. Lupas, Some results of new subclasses for bi-univalent functions using quasi-subordination, Symmetry, (2021), 13(9), 1653, 1-12.

W. G. Atshan, R. A. Al-Sajjad, S. Altinkaya, On the Hankel determinant of m-fold symmetric bi-univalent functions using a new operator, Gazi Univ. J. Sci., 36(1) (2023), 349-360.

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, J. Clunie and W. E. Kirwan, Coefficient estimates for a class of starlike functions, Canad. J. Math., 22 (1970), 476-485.

D. A. Brannan, J. G. Clunie (Eds), Aspects of Contemporary Complex Analysis (Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1 20, 1979), Academic Press, New York and London, 1980.

D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, in: S. M. Mazhar, A. Hamoui, N. S. Faour (Eds), Math. Anal. And Appl., Kuwait; February 18-21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, PP. 53-60. See also Studia Univ. Babe, s-Bolyai Math. 31(2), (1986), 70-77.

Darweesh, A. M.; Atshan, W. G.; Battor, A. H.; Mahdi, M. S. On the third Hankel determinant of certain subclass of bi-univalent functions. Math. Model. Eng. Probl., (2023), 10, 1087-1095.

P. L. Duren, Univalent Functions, In: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Hidelberg and Tokyo, (1983).

B. A. Frasin, M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2011), 1569-1573.

M. Lewin, On a coefficient problem for bi-univalent function, Proceedings of the American Mathematical Society, Vol. 18 (1967), 63-68.

E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Rational Mech., 32 (1969), 100-112.

A ́O Pa ́ll-Szabo, Gl Oros, Coefficient related studies for new classes of bi-univalent functions, mathematics, 2020.

I. A. R. Rahman, W. G. Atshan, G. I. Oros, New concept on fourth Hankel determinant of a certain subclass of analytic functions. Afr. Mat., (2022), 33, 7. 1-15.

P. O. Sabir, H. M. Srivastava, W. G. Atshan, P. O. Mohammed, N. Chorfi and M. V. Cortez, A family of holomorphic and m-fold symmetric bi-univalent functions endowed with coefficient estimate problems, Mathematics, 11(18) (2023), 3970, 1-13.

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

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

F. O. Salman, W. G. Atshan, New results on coefficient estimates for subclasses of bi-univalent functions related by a new integral operator,Int. J. Nonlinear Anal. Appl. 14 (2023) 4, 47-54.

T. S. Taha, Topics in univalent function Theory, Ph.D. Thesis, University of London, 1981.

S. Yalcin, W. G. Atshan, H. Z. Hassan, Coefficients assessment for certain subclasses of bi-univalent functions related with quasi-subordination. Publ. L’Institut Math. Nouv. Se ́r., (2020), 108, 155-162.

Downloads

Published

2024-06-30

How to Cite

Sadiq Jafar, Z., & Galib Atshan, W. (2024). Coefficients Estimates for Certain New Subclasses of Analytic Bi-Univalent Functions. Journal of Al-Qadisiyah for Computer Science and Mathematics, 16(2), Math. 119–125. https://doi.org/10.29304/jqcsm.2024.16.21562

Issue

Section

Math Articles