Maclaurin Coefficient Estimates for a New Subclasses of m-Fold Symmetric Bi-Univalent Functions

  • Abbas Kareem Wanas Department of Mathematics, College of Science, University of Al-Qadisiyah, Iraq
  • Hussein Kadhim Raadhi Department of Mathematics, College of Science, University of Al-Qadisiyah, Iraq
Keywords: analytic functions, univalent functions, bi-univalent functions, m-fold symmetric bi-univalent functions, coefficient estimates

Abstract

In this paper, we obtain upper bounds for the first two Taylor-Maclaurin  and  for two new families Υ_(Σ_m ) (η,γ;α) and Υ_(Σ_m)^* (η,γ;β) of holomorphic and m-fold symmetric bi-univalent functions defined in the open unit disk U. Further, we point out several certain special cases for our results.

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.

I. Aldawish, S. R. Swamy and B. A. Frasin, A special family of m-fold symmetric bi-univalent functions satisfying subordination condition, Fractal Fractional 6 (2022), 271. https://doi.org/10.3390/fractalfract6050271

S. Altinkaya and S. Yalçin, Coefficient bounds for certain subclasses of m-fold symmetric bi-univalent functions, Journal of Mathematics 2015 (2015), Art. ID 241683, 1-5. https://doi.org/10.1155/2015/241683

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. https://doi.org/10.1501/Commua1_0000000827

A. Amourah, A. Alamoush, and M. Al-Kaseasbeh, Gegenbauer polynomials and bi univalent functions, Palestine Journal of Mathematics 10(2) (2021), 625-632. https://doi.org/10.3390/math10142462

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, Coefficient estimates for general subclasses of m-fold symmetric analytic biunivalent functions, Turkish J. Math. 40 (2016), 1386-1397. https://doi.org/10.3906/mat-1511-41

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. https://doi.org/10.3906/mat-1503-58

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

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. https://doi.org/10.1016/j.joems.2012.08.020

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. https://doi.org/10.1090/S0002-9939-1989-0930244-7

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. https://doi.org/10.32513/tbilisi/1524276036

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.

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. https://doi.org/10.1016/j.joems.2014.04.002

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. https://doi.org/10.2298/FIL1305831S

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. https://doi.org/10.2298/FIL1508839S

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. https://doi.org/10.1016/S0252-9602(16)30045-5

H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188-1192. https://doi.org/10.1016/j.aml.2010.05.009

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. https://doi.org/10.2478/tmj-2014-0011

H. M. Srivastava and A. K. Wanas, Initial Maclaurin coefficient bounds for new subclassesof analytic and m-fold symmetric bi-univalent functions defined by a linear combination, Kyungpook Math. J. 59 (2019), 493-503.

H. M. Srivastava, A. K. Wanas and G. Murugusundaramoorthy, Certain family of biunivalent functions associated with Pascal distribution series based on Horadam polynomials, Surveys Math. Appl. 16 (2021), 193-205.

S. R. Swamy and L-I. Cotîrlă, On τ-Pseudo-v-convex κ-fold symmetric bi-univalent function family, Symmetry 14(10) (2022), 1972. https://doi.org/10.3390/sym14101972

S. R. Swamy, B. A. Frasin and I. Aldawish, Fekete-Szegö functional problem for a special family of m-fold symmetric bi-univalent functions, Mathematics 10 (2022), 1165. https://doi.org/10.3390/math10071165

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. https://doi.org/10.7153/jmi-10-85

A. K. Wanas and H. Tang, Initial coefficient estimates for a classes of m-fold symmetric bi-univalent functions involving Mittag-Leffler function, Mathematica Moravica 24(2) (2020), 51-61. https://doi.org/10.5937/MatMor2002051K

Published
2022-10-18
How to Cite
WanasA. K., & RaadhiH. K. (2022). Maclaurin Coefficient Estimates for a New Subclasses of m-Fold Symmetric Bi-Univalent Functions. Earthline Journal of Mathematical Sciences, 11(2), 199-210. https://doi.org/10.34198/ejms.11223.199210
Section
Articles