SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 6

Faber polynomials coefficients estimates for a certain subclass of Bazilevic functions

Abdel Moneim Lashin
Abeer O. Badghaish
Amani Z. Bajamal
Pages
1667–1678
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Moreover, some special cases are also indicated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:For a certain subclass of Bazilevic functions, Faber polynomials expansions are used to obtain bi-univalent properties.
📊
Key Findings & Data:Estimates on the $n$th Taylor-Maclaurin coefficients of functions in this class are found.
💡
Conclusion & Impact:Moreover, some special cases are also indicated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Faber polynomial · Bazilevic functions · coefficient estimations

Abstract

For a certain subclass of Bazilevic functions, Faber polynomials expansions are used to obtain bi-univalent properties. Estimates on the $n$th Taylor-Maclaurin coefficients of functions in this class are found. Moreover, some special cases are also indicated.

🔖

Cite This Article

Lashin, A. M., Badghaish, A. O., Bajamal, A. Z. (2022). Faber polynomials coefficients estimates for a certain subclass of Bazilevic functions. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1667–1678. https://ajindex.com/articles/529511

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math. 130, 179–222, 2006
  2. H. Airault and J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math. 126, 343–367, 2002
  3. S. Altınkaya, Bounds for a new subclass of bi-univalent functions subordinate to the Fibonacci numbers, Turkish J. Math. 44 (2), 553–560, 2020
  4. S. Altınkaya and S. Yalcın, Faber polynomial coefficient bounds for a subclass of bi- univalent functions, C. R. Math. 353 (12), 1075–108, 2015
  5. A. Bouali, Faber polynomials, Cayley-Hamilton equation and Newton symmetric func- tions, Bull. Sci. Math. 130, 49–70, 2006
  6. M. Caglar, H. Orhan and N. Yagmur, Coefficient bounds for new subclasses of bi- univalent functions, Filomat, 27 (7), 1165–1171, 2013
  7. E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate condi- tions, J. Class. Anal. 2, 49–60, 2013
  8. E. Deniz, J.M. Jahangiri, S.G. Hamidi and S.K. Kina, Faber polynomial coefficients for generalized bi-subordinate functions of complex order, J. Math. Inequal. 12 (3), 645–653, 2018
  9. P.L. Duren, Univalent Functions, Grundlehren Math. Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983
  10. G. Faber, Über polynomische Entwickelungen, Math. Ann. doi: 10.1007/BF01444293, 1903
  11. P. Goel and S.S. Kumar, Certain class of starlike functions associated with modified sigmoid function, Bull. Malays. Math. Sci. Soc. 43, 957–991, 2020
  12. S.P. Goyal and R. Kumar, Coefficient estimates and quasi-subordination properties associated with certain subclasses of analytic and bi-univalent functions, Math. Slo- vaca, 65 (3), 533–544, 2015
  13. T. Hayami and S. Owa, Coefficient bounds for bi-univalent functions, Pan Amer. Math. J. 22 (4), 15–26, 2012
  14. S. Kanas, V.S. Masih and A. Ebadian, Relations of a planar domain bounded by hyperbola with family of holomorphic functions, J. Inequl. Appl. 246, 1–14, 2019
  15. A.Y. Lashin, On certain subclasses of analytic and bi-univalent functions, J. Egyptian Math. Soc. 24 (2), 220–225, 2016
  16. A.Y. Lashin, Coefficient estimates for two subclasses of analytic and bi-univalent functions, Ukr. Math. J. 70 (9), 1484–1492, 2019
  17. A.Y. Lashin and F.Z. EL-Emam, Faber polynomial coefficients for certain subclasses of analytic and biunivalent functions, Turkish J. Math. 44, 1345–1361, 2020
  18. M. Lewin, On a coefficient problem for