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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Volume: 50 Issue: 6

Faber polynomials coefficients estimates for a certain subclass of Bazilevic functions

Abdel Moneim Lashin(King Abdulaziz University)0000-0002-0694-4358
Abeer Badghaish(King Abdulaziz University)0000-0001-7498-2228
Amani Bajamal(King Abdulaziz University)0000-0003-1708-2228
Pages
—
Publication Date
2021-12-14
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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.
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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.

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Cite This Article

Lashin, A. M., Badghaish, A., Bajamal, A. (2021). Faber polynomials coefficients estimates for a certain subclass of Bazilevic functions. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 6. https://doi.org/10.15672/hujms.896977

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References (29)

  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 bi-univalent functions, Proc. Amer. Math. Soc. 18, 63–68, 1967.
  19. N. Magesh, T. Rosy and S. Varma, Coefficient estimate problem for a new subclass of bi-univalent functions, J. Complex Anal. 2013, Art. ID 474231, 3pp., 2013.
  20. N. Magesh and J. Yamini, Coefficient bounds for certain subclasses of bi-univalent functions, Int. Math. Forum, 8, 1337–1344, 2013.
  21. R. Mendiratta, S. Nagpal and V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc. 38 (1), 365–386, 2015.
  22. G. Murugusundaramoorthy, N. Magesh and V. Prameela, Coefficient bounds for cer- tain subclasses of bi-univalent function, Abstr. Appl. Anal. Art. ID 573017, 3 pp., 2013.
  23. Z.-G. Peng and Q.-Q. Han, On the coefficients of several classes of bi-univalent func- tions, Acta Math. Sci. Ser. B Engl. Ed. 34, 228–240, 2014.
  24. S. Porwal and M. Darus, On a new subclass of bi-univalent functions, J. Egypt. Math. Soc. 21 (3), 190–193, 2013.
  25. R.K. Raina and J. Sokół, Some properties related to a certain class of starlike func- tions, C. R. Acad. Sci. Paris Ser. I 353 (11), 973–978, 2015.
  26. J. Sokół and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. 19, 101–105, 1996.
  27. H.M. Srivastava, S. Bulut, M. Caglar and N. Yagmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27 (5), 831–842, 2013.
  28. A. Zireh, E.A. Adegani and M. Bidkham, Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate, Math. Slovaca, 68 (2), 369–378, 2018.
  29. Z-G.Wang and Y-P. Jiang, Notes on certain subclass of p-valently Bazilevic functions, J. Inequl. Pure Appl. Math. 9 (3), Art. 70, 7pp., 2008.