Journals / Conference Proceedings of Science and Technology / 2026 / Cilt: 2 Sayı: 1

Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator

Pages
9–12
Publication Date
2019-10-30
DOI
—
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AI Summary & Key Takeaways

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

The results presented here generalize some of the earlier studies.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, we construct a new subclass of $m$-fold symmetric bi-univalent functions using by Hadamard product and generalized Salagean differential operator in the open unit disk $U=\left\{ z\in \mathbb{C} :\left\vert z\right\vert <1\right\} $.
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Key Findings & Data:We establish upper bounds for the coefficients $\left\vert a_{m+1}\right\vert $ and $\left\vert a_{2m+1}\right\vert $ belonging to this new class.
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Conclusion & Impact:The results presented here generalize some of the earlier studies.
🔬Design:Konferans Bildirisi
📍Scope:Comprehensive Sample
⚙️Variables:Coefficient estimates · bi-univalent functions · m-fold symmetric functions

Abstract

In this study, we construct a new subclass of $m$-fold symmetric bi-univalent functions using by Hadamard product and generalized Salagean differential operator in the open unit disk $U=\left\{ z\in \mathbb{C} :\left\vert z\right\vert <1\right\} $. We establish upper bounds for the coefficients $\left\vert a_{m+1}\right\vert $ and $\left\vert a_{2m+1}\right\vert $ belonging to this new class. The results presented here generalize some of the earlier studies.

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Cite This Article

Sakar, F. M., Aydoğan, S. M., Altınkaya, Ş. (2019). Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator. Conference Proceedings of Science and Technology, Cilt: 2 Sayı: 1, 9–12. https://ajindex.com/articles/1648746

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References (12)

  1. F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci., 27 (2004), 1429-1436.
  2. D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babe¸s-Bolyai Mathematica, 31 (1986), 70-77.
  3. S. Bulut, Coefficient estimates for general subclasses ofm-fold symmetric analytic bi-univalent functions, Turkish J. Math., 40 (2016), 1386-1397.
  4. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA 259, 1983.
  5. S. G. Hamidi, J. M. Jahangiri, Unpredictability of the coefficients ofm-fold symmetric bi-starlike functions, Internat. J. Math., 25 (2014), 1-8.
  6. M. Lewin, On a coefficient problem for bi-univalent functions, Proceedings of the American Mathematical Society, 18 (1967), 63-68.
  7. E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in jzj < 1, Archive for Rational Mechanics and Analysis, 32 (1969), 100-112.
  8. Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Gottingen, 1975.
  9. G. S. Salagean, Subclasses of univalent functions, in Complex Analysis, Fifth Romanian Finish Seminar, Part 1 (Bucharest, 1981), 1013 of Lecture Notes in Mathematics, 362-372, Springer, Berlin, Germany, 1983.
  10. H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Applied Mathematics Letters, 23 (2010), 1188-1192.
  11. H. M. Srivastava, S. Sivasubramanian, R. Sivakumar, Initial coefficient bounds for a subclass ofm-fold symmetric bi-univalent functions, Tbilisi Mathematical Journal, 7 (2014), 1-10.
  12. S. Sumer Eker, Coefficient bounds for subclasses ofm-fold symmetric bi-univalent functions, Turkish J. Math., 40 (2016), 641-646.