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Journals / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 12 Issue: 2

On the Coefficent Bound Estimates and Fekete-Szegö Problem

Nizami Mustafa(KAFKAS ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0002-2758-0274
Semra Korkmaz(KAFKAS ÜNİVERSİTESİ)0000-0002-7846-9779
Pages
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Publication Date
2023-06-27
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some interesting special cases of the results obtained here are also discussed.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we introduce and examine a certain subclass of analytic functions in the open unit disk in the complex plane.
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Key Findings & Data:Here, we give coefficient bound estimates and investigate the Fekete-Szegö problem for the introduced class.
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Conclusion & Impact:Some interesting special cases of the results obtained here are also discussed.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Coefficient estimates · Fekete-Szegö problem · Analytic function

Abstract

In this study, we introduce and examine a certain subclass of analytic functions in the open unit disk in the complex plane. Here, we give coefficient bound estimates and investigate the Fekete-Szegö problem for the introduced class. Some interesting special cases of the results obtained here are also discussed.

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Cite This Article

Mustafa, N., Korkmaz, S. (2023). On the Coefficent Bound Estimates and Fekete-Szegö Problem. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 12 Issue: 2. https://doi.org/10.17798/bitlisfen.1194877

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References (22)

  1. M. Buyankara, M. Çağlar, L.-I. Cotîrlă, “New subclasses of bi-univalent functions with respect to the symmetric points defined by bernoulli polynomials”, Axioms, vol.11, no.11, pp. 652-660, 2022.
  2. D. A. Brannan and J. Clunie, “Aspects of Contemporary Complex Analysis”, Academic Press, London and New York, USA, 1980.
  3. D. A. Brannan and T. S. Taha, “On Some Classes of Bi-univalent Functions”, Studia Univ. Babes-Bolyai Mathematics, vol. 31, pp.70-77, 1986.
  4. Y. Cheng, R. Srivastava, J. L. Liu, “Applications of the q-derivative operator to new families of bi-univalent functions related to the Legendre Polynomials”, Axioms, vol. 11, no.11, pp. 595-607, 2022.
  5. J. Dziok, “Classes of meromorphic harmonic functions defined by Sălăgean operator”, Revista de la Real Academia de Ciencias Exactas, Físicay Naturales. Serie A. Matemáticas, vol. 116, no.4, pp.1-16, 2022.
  6. P. L. Duren, “Univalent Functions”, In: Grundlehren der Mathematischen Wissenschaften, Band 259, New- York, Berlin, Heidelberg and Tokyo, Springer-Verlag, 1983.
  7. M. Fekete and G. Szegö, “Eine Bemerkung über ungerade schlichte funktionen”, Journal of the London Mathematical Society, vol.8, pp.85-89, 1993.
  8. U. Grenander and G. Szegö, “Toeplitz form and their applications”, California Monographs in Mathematical Sciences, University California Press, Berkeley, 1958.
  9. H.Ö. Güney, G.I. Oros, S. Owa, “An Application of Sălăgean operator concerning starlike functions”, Axioms, vol. 11, no.2, pp. 50-59, 2022.
  10. M. Lewin, “On a coefficient problem for bi-univalent functions”, Proceedings of the American Mathematical Society, vol.18, pp.63-68, 1967.
  11. S. Li, L. Ma, H. Tang, “On Janowski type p-harmonic functions associated with generalized Sălăgean operator”, AIMS Mathematics, vol. 6, no.1, pp.569-583, 2021.
  12. N. Mustafa, “Fekete- Szegö problem for certain subclass of analytic and bi-univalent functions”, Journal of Scientific and Engineering Research, vol.4, no.8, pp.30-400, 2017.
  13. N. Mustafa and M. C. Gündüz, “The Fekete-Szegö problem for certain class of analytic and univalent functions”, Journal of Scientific and Engineering Research, vol.6, no.5, pp.232-239, 2019.
  14. N. Mustafa and G. Murugusundaramoorthy, “Second Hankel for mocanu type bi-starlike functions related to shell shaped region”, Turkish Journal of Mathematics, vol.45, pp.1270-1286, 2021.
  15. E. Netanyahu, “The minimal distance of the image boundary from the origin and the second coefficient of a univalent function”, Archive for Rational Mechanics and Analysis, vol.32, pp.100-112, 1969.
  16. G.I. Oros, L.-I. Cotîrlă, “Coefficient Estimates and the Fekete–Szegö problem for new classes of m-fold symmetric bi-univalent functions”, Mathematics, vol. 10, pp. 129-141, 2022. https://doi.org/10.3390/math10010129
  17. Á.O. Páll-Szabó, G. I. Oros, “Coefficient related studies for new classes of bi-univalent functions”, Mathematics, vol. 8, no.7, pp. 1110-1123, 2020.
  18. G. S. Sălăgean, “Subclasses of univalent functions”, Complex Analysis, vol.103, pp.362-372, 1983.
  19. H. M. Srivastava, A. K. Mishra and P. Gochhayat, “Certain sublcasses of analytic and bi-univalent functions”, Applied Mathematics Letters, vol.23, pp.1188-1192, 2010.
  20. H. M. Srivastava, G. Murugusundaramoorthy, T. Bulboacă, “The second Hankel determinant for subclasses of bi-univalent functions associated with a nephroid domain”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Mathemáticas, vol. 116, no.4, 1-21, 2022.
  21. P. Zaprawa, “On the Fekete-Szegö problem for the classes of bi-univalent functions”, Bulletin of the Belgain Mathematical Society, vol.21, pp.169-178, 2014.
  22. Q. H. Xu, G. Xiao and H. M. Srivastava, “A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems”, Applied Mathematics and Computation, vol. 218, pp.11461-11465, 2012.