On coefficient estimate of K-fold bi-univalent functions
*Hadeel K. AboodCorresponding authorhad23u2005@uoanbar.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of AnbarAnbar, IraqView full profile → , Abdul Rahman S. Jumaeps.abdulrahman.juma@uoanbar.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of AnbarAnbar, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Mar 2025
- Published Online:
- 29 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2247
- Pages:
- 413–421
Abstract
Keywords
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References
[1] P. L. Duren, Univalent Functions, vol. 259. New York, NY, USA: Springer (2001).
[2] M. Lewin, “On a coefficient problem for bi-univalent functions,” Proc. Amer. Math. Soc., vol. 18, no. 1, pp. 63–68 (1967).
[3] D. A. Brannan and 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. New York, NY, USA: Academic Press (1980).
[4] H. M. Srivastava, A. K. Mishra, and P. Gochhayat, “Certain subclasses of analytic and bi-univalent functions,” Appl. Math. Lett., vol. 23, no. 10, pp. 1188–1192 (2010).
[5] S. Bulut, “Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions,” Turk. J. Math., vol. 40, no. 6, pp. 1386–1397 (2016).
[6] E. A. Adegani, S. Bulut, and A. Zireh, “Coefficient estimates for a subclass of analytic bi-univalent functions,” Bull. Korean Math. Soc., vol. 55, no. 2, pp. 405–413 (2018).
[7] H. Ö. Güney, G. Murugusundaramoorthy, and J. Sokół, “Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers,” Acta Univ. Sapientiae, Math., vol. 10, no. 1, pp. 70–84 (2018).
[8] H. Orhan, N. Magesh, and J. Yamini, “Coefficient estimates for a class of bi-univalent functions associated with quasi-subordination,” Creat. Math. Inform., vol. 26, no. 2, pp. 193–199 (2017).
[9] M. Haji Mohd and M. Darus, “Fekete-Szegö problems for quasi-subordination classes,” Abstr. Appl. Anal., vol. 2012, no. 1, pp. 1–12 (2012).
[10] H. M. Srivastava, S. Gaboury, and F. Ghanim, “Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions,” Acta Univ. Apulensis Math. Inform., no. 41, pp. 153–164 (2015).
[11] A. M. Delphi and K. A. Jassim, “New subclasses for estimates coefficients of m-fold symmetric bi-univalent functions and Fekete-Szegö problems,” J. Interdiscip. Math., vol.25 , no. 6, pp. 1857–1867 (2022).
[12] H. M. Srivastava, S. Sivasubramanian, and R. Sivakumar, “Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions,” Tbilisi Math. J., vol. 7, no.2 , pp. 1–10 (2014).
[13] N. H. Shehab and A. R. S. Juma, “Coefficient bounds of m-fold symmetric bi-univalent functions for certain subclasses,” Int. J. Nonlinear Anal. Appl., vol.12, pp. 71–82 (2021).
[14] A. R. S. Juma, A. Al-Fayadh, and N. H. Shehab, “Estimates of coefficient for certain subclasses of k-fold symmetric bi-univalent functions,” Iraqi J. Sci., vol. 63, no. 5, pp. 2155–2163 (2022).
[15] A. R. S. Juma, A. Al-Fayadh, S. P. Vijayalakshmi, and T. V. Sudharsan, “Upper bound on the third Hankel determinant for the class of univalent functions using an integral operator,” Afr. Mat., vol. 33, no.2, p. 56 (2022).
[16] Abbood, Mohaimen M., Ebrahim, Hassan H., Al-Fayadh, Ali & Obaid, Ahmed J. Measure defined on & Gamma; – algebra and some of their generalizations, Journal of Interdisciplinary Mathematics, 26:5, 821–827 (2023), DOI: 10.47974/JIM-1502.
[17] S. R. Swamy and L. I. Cotîrlă, “A new pseudo-type κ-fold symmetric bi-univalent function class,” Axioms, vol. 12, no. 10, Art. no. 953 (Oct. 2023).
[18] C. Pommerenke, Univalent Functions. Göttingen, Germany: Vandenhoeck & Ruprecht (1975).




