Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 75 Issue: 1

Coefficient Estimates for a Novel Subclass of Analytic and Biunivalent Functions

Seyed Hadi Hosseini(Shahrood University of Technology)0009-0002-0099-1468
Ahmad Motamednezhad(Shahrood University of Technology)0000-0001-6844-129X
Sayfa
—
Yayın Tarihi
2026-03-29
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The results, presented in this study extend and enhance several recent works by earlier authors.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper introduces and explores a novel subclass $\mathcal{R}_{\Sigma}^{h,p}(\lambda,\gamma)$ of bi-univalent functions within the open unit disk $\mathbb{U}$.
📊
Temel Bulgular & Veri:We establish upper bounds for the second, third, and fourth coefficients of functions belonging to this class.
💡
Sonuç & Katkı:The results, presented in this study extend and enhance several recent works by earlier authors.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Analytic functions · coefficient estimates · starlike functions

Abstract

This paper introduces and explores a novel subclass $\mathcal{R}_{\Sigma}^{h,p}(\lambda,\gamma)$ of bi-univalent functions within the open unit disk $\mathbb{U}$. We establish upper bounds for the second, third, and fourth coefficients of functions belonging to this class. Furthermore, we derive estimates for the Fekete-Szegö problem in this context. The results, presented in this study extend and enhance several recent works by earlier authors.

🔖

Bu Makaleye Atıf Yap

Hosseini, S. H., Motamednezhad, A. (2026). Coefficient Estimates for a Novel Subclass of Analytic and Biunivalent Functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 75 Issue: 1. https://doi.org/10.31801/cfsuasmas.1637685

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (25)

  1. Brannan, D. A. and Clunie, J. G. (1980). Aspects of contemporary complex analysis. In Proceedings of the NATO Advanced Study Institute. Academic Press, New York and London. University of Durham, July 1–20, 1979.
  2. Brannan, D. A. and Taha, T. S. (1986). On some classes of bi-univalent functions. Studia Universitatis Babes-Bolyai Mathematica, 31:70–77.
  3. Duren, P. L. (1983). Univalent Functions. Springer-Verlag, New York and Berlin.
  4. Fekete, M. and Szegö, G. (1933). Eine bemerkung über ungerade schlichte funktionen. Journal of the London Mathematical Society, 1:85–89.
  5. Frasin, B. A. (2014). Coefficient bounds for certain classes of bi-univalent functions. Hacettepe Journal of Mathematics and Statistics, 43:383–389.
  6. Frasin, B. A. and Aouf, M. K. (2011). New subclasses of bi-univalent functions. Applied Mathematics Letters, 24:1569–1573.
  7. Gao, C. Y. and Zhou, S. Q. (2007). Certain subclass of starlike functions. Applied Mathematics and Computation, 187:176–182.
  8. Gulec, H. H. and Aktas, I. (2024). Coefficient estimate problems for a new subclass of bi-univalent functions linked with the generalized bivariate Fibonacci-like polynomial. Journal of Engineering Technology and Applied Sciences, 9:71–84.
  9. Hayami, T. and Owa, S. (2012). Coefficient bounds for bi-univalent functions. Pan American Mathe- matical Journal, 22:15–26.
  10. Kedzierzawski, A. W. (1985). Some remarks on bi-univalent functions. Annales Universitatis Mariae Curie-Sklodowska, Sectio A, 39:77–81.
  11. Lewin, M. (1967). On a coefficient problem for bi-univalent functions. Proceedings of the American Mathematical Society, 18:63–68.
  12. Magesh, N., Rosy, T., and Varma, S. (2013). Coefficient estimate problem for a new subclass of bi-univalent functions. Journal of Complex Analysis, 2013:474231.
  13. Magesh, N. and Yamini, J. (2014). Coefficient estimates for a certain general subclass of analytic and bi-univalent functions. Applied Mathematics, 5:1047–1052.
  14. Magesh, N. and Yamini, J. (2018). Fekete-Szego problem and second Hankel determinant for a class of bi-univalent functions. Tbilisi Mathematical Journal, 11:141–157.
  15. Motamednezhad, A., Nosrati, S., and Zaker, S. (2019). Bounds for initial Maclaurin coefficients of a subclass of bi-univalent functions associated with subordination. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68:125–135.
  16. Nazmiye, Y. and Aktas, I. (2022). On some new subclasses of bi-univalent functions defined by generalized bivariate Fibonacci polynomial. Afrika Matematika, 33:59.
  17. Orhan, H., Aktas, I., and Arikan, H. (2023). On a new subclass of biunivalent functions associated with the $(p,q)$-Lucas polynomials and bi-Bazilevic type functions of order $\rho + i\xi$}. Turkish Journal of Mathematics, 47:98–109.
  18. Ozturk, R. and Aktas, I. (2024). Coefficient estimate and Fekete-Szegö problems for certain new subclasses of bi-univalent functions defined by generalized bivariate Fibonacci polynomial. Sahand Communications in Mathematical Analysis, 21:35–53.
  19. Patil, A. B. (2022). Sharp coefficient inequalities for certain subclasses of bi-univalent Bazilevic functions. Communications of the Korean Mathematical Society, 37:113–123.
  20. Srivastava, H. M., Mishra, A. K., and Gochhayat, P. (2010). Certain subclasses of analytic and biunivalent functions. Applied Mathematics Letters, 23:1188–1192.
  21. Tan, D. L. (1984). Coefficient estimates for bi-univalent functions. Chinese Annals of Mathematics, Series A, 5:559–568.
  22. Xu, Q. H., Gui, Y. C., and Srivastava, H. M. (2012a). Coefficient estimates for a certain subclass of analytic and bi-univalent functions. Applied Mathematics Letters, 25:990–994.
  23. Xu, Q. H., Xiao, H. G., and Srivastava, H. M. (2012b). A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems. Applied Mathematics and Computation, 218:11461–11465.
  24. Zaprawa, P. (2014). On the Fekete-Szegö problem for classes of bi-univalent functions. Bulletin of the Belgian Mathematical Society Simon Stevin, 21:169–178.
  25. Zireh, A. and Audegani, E. A. (2016). Coefficient estimates for a subclass of analytic and bi-univalent functions. Bulletin of the Iranian Mathematical Society, 42:881–889.