Research Article

Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $

Volume: 8 Number: 1 March 20, 2020
EN

Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $

Abstract

In this present investigation, based on the $(p,q)$-Lucas polynomials, we
want to build a bridge between the Theory of Geometric Functions and that of
Special Functions, which are usually considered as very different fields.

Keywords

(p¸ q)-Lucas polynomials,coefficient bounds,bi-univalent functions,Fekete-Szegö inequalities

References

  1. \bibitem{AY} Alt\i nkaya, \c{S}. and Yal\c{c}\i n, S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions. \emph{C.R. Acad. Sci. Paris, Ser. I} 353 (2015), no. 12, 1075-1080.
  2. \bibitem{Altinkaya-and-Yalcin2014b} Alt\i nkaya, \c{S}. and Yal\c{c}\i n, S., Fekete-Szeg\"{o} inequalities for certain classes of bi-univalent functions. \emph{Internat. Scholar. Res. Notices} 2014 (2014), 1-6, Article ID 327962.
  3. \bibitem{BT} Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions. \emph{Studia Universitatis Babe\c{s}-Bolyai Mathematica} 31 (1986), 70-77.
  4. \bibitem{dur} Duren, P. L., Univalent Functions. Grundlehren der Mathematischen Wissenschaften, Bd. 259, Springer-Verlag, Berlin, Heidelberg, New York and Tokyo, 1983.
  5. \bibitem{Fekete-and-Szego33} Fekete, M. and Szeg\"{o}, G., Eine Bemerkung Über Ungerade Schlichte Funktionen. \emph{J. London Math. Soc.} [s1-8(2)] (1933), 85--89.
  6. \bibitem{L} Lewin, M., On a coefficient problem for bi-univalent functions. \emph{Proc. Amer. Math. Soc.} 18 (1967), 63-68.
  7. \bibitem{lee} Lee, G. Y. and A\c{s}c\i, M., Some properties of the $(p,q) $-Fibonacci and $(p,q)$-Lucas polynomials. \emph{Journal of Applied Mathematics} 2012 (2012), 1-18, Article ID 264842.
  8. \bibitem{lon} London, R. R. and Thomas, D. K., The derivative of Bazilevi$\breve{c}$ functions. \emph{Proc. Amer. Math. Soc.} 104 (1988), 235-238.
  9. \bibitem{lup} Lupas, A., A guide of Fibonacci and Lucas polynomials. \emph{Octagon Mathematics Magazine} 7 (1999), 2--12.
  10. \bibitem{mac} MacGregor, T. H., Functions whose derivative has a positive real part. \emph{Trans. Amer. Math. Soc.} 104 (1962), 532--537.
APA
Altınkaya, S., & Yalçın, S. (2020). Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $. Mathematical Sciences and Applications E-Notes, 8(1), 134-141. https://doi.org/10.36753/mathenot.650271
AMA
1.Altınkaya S, Yalçın S. Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $. Math. Sci. Appl. E-Notes. 2020;8(1):134-141. doi:10.36753/mathenot.650271
Chicago
Altınkaya, Sahsene, and Sibel Yalçın. 2020. “Some Applications of the (p,q)-Lucas Polynomials to the Bi-Univalent Function Class $\Sigma $”. Mathematical Sciences and Applications E-Notes 8 (1): 134-41. https://doi.org/10.36753/mathenot.650271.
EndNote
Altınkaya S, Yalçın S (March 1, 2020) Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $. Mathematical Sciences and Applications E-Notes 8 1 134–141.
IEEE
[1]S. Altınkaya and S. Yalçın, “Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 134–141, Mar. 2020, doi: 10.36753/mathenot.650271.
ISNAD
Altınkaya, Sahsene - Yalçın, Sibel. “Some Applications of the (p,q)-Lucas Polynomials to the Bi-Univalent Function Class $\Sigma $”. Mathematical Sciences and Applications E-Notes 8/1 (March 1, 2020): 134-141. https://doi.org/10.36753/mathenot.650271.
JAMA
1.Altınkaya S, Yalçın S. Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $. Math. Sci. Appl. E-Notes. 2020;8:134–141.
MLA
Altınkaya, Sahsene, and Sibel Yalçın. “Some Applications of the (p,q)-Lucas Polynomials to the Bi-Univalent Function Class $\Sigma $”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, Mar. 2020, pp. 134-41, doi:10.36753/mathenot.650271.
Vancouver
1.Sahsene Altınkaya, Sibel Yalçın. Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $. Math. Sci. Appl. E-Notes. 2020 Mar. 1;8(1):134-41. doi:10.36753/mathenot.650271

Cited By

(U; V )-Lucas polynomial coefficient relations of the bi-univalent function class

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics

https://doi.org/10.31801/cfsuasmas.1086809