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

Year 2020, Volume: 8 Issue: 1, 134 - 141, 20.03.2020

Sahsene Altınkaya Sibel Yalçın

https://doi.org/10.36753/mathenot.650271
Cited By: 1

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

  • \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.
  • \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.
  • \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.
  • \bibitem{dur} Duren, P. L., Univalent Functions. Grundlehren der Mathematischen Wissenschaften, Bd. 259, Springer-Verlag, Berlin, Heidelberg, New York and Tokyo, 1983.
  • \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.
  • \bibitem{L} Lewin, M., On a coefficient problem for bi-univalent functions. \emph{Proc. Amer. Math. Soc.} 18 (1967), 63-68.
  • \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.
  • \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.
  • \bibitem{lup} Lupas, A., A guide of Fibonacci and Lucas polynomials. \emph{Octagon Mathematics Magazine} 7 (1999), 2--12.
  • \bibitem{mac} MacGregor, T. H., Functions whose derivative has a positive real part. \emph{Trans. Amer. Math. Soc.} 104 (1962), 532--537.
  • \bibitem{N} Netanyahu, E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in $\left\vert z\right\vert <1$. \emph{Archive for Rational Mechanics and Analysis} 32 (1969), 100-112.
  • \bibitem{oz} \"{O}zko\c{c}, A. and Porsuk, A., A note for the $(p,q)$-Fibonacci and Lucas quaternion polynomials. \emph{Konuralp Journal of Mathematics} 5 (2017), no. 2, 36--46.
  • \bibitem{plip} Filipponi, P. and Horadam, A. F., Derivative sequences of Fibonacci and Lucas polynomials. In: Applications of Fibonacci Numbers, Springer, Dordrecht, 1991.
  • \bibitem{SGM} Srivastava, H. M., Murugusundaramoorthy, G. and Magesh, N., Certain subclasses of bi-univalent functions associated with the Hohlov operator. \emph{Applied Mathematics Letters} 1 (2013), 67-73.
  • \bibitem{Singh 73} Singh, R., On Bazilevi$\breve{c}$ functions. \emph{Proc. Amer. Math. Soc.} 38 (1973), 261-271.
  • \bibitem{SMG} Srivastava, H. M., Mishra, A. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions. \emph{Applied Mathematics Letters} 23 (2010), 1188-1192.
  • \bibitem{Srivastava-Fekete} Srivastava, H. M., Mishra, A. K. and Das, M. K., The Fekete-Szeg\"{o} problem for a subclass of close-to-convex functions. \emph{Complex Variables Theory Appl.} 44 (2001), no. 2, 145--163.
  • \bibitem{vel} Vellucci, P. and Bersani, A.M., The class of Lucas-Lehmer polynomials. \emph{Rendiconti di Matematica} 37 (2016), no. 1-2, 43-62.
  • \bibitem{wa} Wang, T. and Zhang, W., Some identities involving Fibonacci, Lucas polynomials and their applications. \emph{Bull. Math. Soc. Sci. Math. Roum.} 55 (2012), no. 1, 95-103.
  • \bibitem{Zaprawa2014} Zaprawa, Z., On Fekete-Szeg\"{o} problem for classes of bi-univalent functions. \emph{Bull. Belg. Math. Soc. Simon Stevin} 21 (2014), 169--178.

Year 2020, Volume: 8 Issue: 1, 134 - 141, 20.03.2020

Sahsene Altınkaya Sibel Yalçın

https://doi.org/10.36753/mathenot.650271
Cited By: 1

Abstract

References

  • \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.
  • \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.
  • \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.
  • \bibitem{dur} Duren, P. L., Univalent Functions. Grundlehren der Mathematischen Wissenschaften, Bd. 259, Springer-Verlag, Berlin, Heidelberg, New York and Tokyo, 1983.
  • \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.
  • \bibitem{L} Lewin, M., On a coefficient problem for bi-univalent functions. \emph{Proc. Amer. Math. Soc.} 18 (1967), 63-68.
  • \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.
  • \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.
  • \bibitem{lup} Lupas, A., A guide of Fibonacci and Lucas polynomials. \emph{Octagon Mathematics Magazine} 7 (1999), 2--12.
  • \bibitem{mac} MacGregor, T. H., Functions whose derivative has a positive real part. \emph{Trans. Amer. Math. Soc.} 104 (1962), 532--537.
  • \bibitem{N} Netanyahu, E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in $\left\vert z\right\vert <1$. \emph{Archive for Rational Mechanics and Analysis} 32 (1969), 100-112.
  • \bibitem{oz} \"{O}zko\c{c}, A. and Porsuk, A., A note for the $(p,q)$-Fibonacci and Lucas quaternion polynomials. \emph{Konuralp Journal of Mathematics} 5 (2017), no. 2, 36--46.
  • \bibitem{plip} Filipponi, P. and Horadam, A. F., Derivative sequences of Fibonacci and Lucas polynomials. In: Applications of Fibonacci Numbers, Springer, Dordrecht, 1991.
  • \bibitem{SGM} Srivastava, H. M., Murugusundaramoorthy, G. and Magesh, N., Certain subclasses of bi-univalent functions associated with the Hohlov operator. \emph{Applied Mathematics Letters} 1 (2013), 67-73.
  • \bibitem{Singh 73} Singh, R., On Bazilevi$\breve{c}$ functions. \emph{Proc. Amer. Math. Soc.} 38 (1973), 261-271.
  • \bibitem{SMG} Srivastava, H. M., Mishra, A. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions. \emph{Applied Mathematics Letters} 23 (2010), 1188-1192.
  • \bibitem{Srivastava-Fekete} Srivastava, H. M., Mishra, A. K. and Das, M. K., The Fekete-Szeg\"{o} problem for a subclass of close-to-convex functions. \emph{Complex Variables Theory Appl.} 44 (2001), no. 2, 145--163.
  • \bibitem{vel} Vellucci, P. and Bersani, A.M., The class of Lucas-Lehmer polynomials. \emph{Rendiconti di Matematica} 37 (2016), no. 1-2, 43-62.
  • \bibitem{wa} Wang, T. and Zhang, W., Some identities involving Fibonacci, Lucas polynomials and their applications. \emph{Bull. Math. Soc. Sci. Math. Roum.} 55 (2012), no. 1, 95-103.
  • \bibitem{Zaprawa2014} Zaprawa, Z., On Fekete-Szeg\"{o} problem for classes of bi-univalent functions. \emph{Bull. Belg. Math. Soc. Simon Stevin} 21 (2014), 169--178.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Sahsene Altınkaya

Sibel Yalçın

Publication Date March 20, 2020
Submission Date January 24, 2019
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

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 Altınkaya S, Yalçın S. Some Applications of the (p,q)-Lucas Polynomials to the bi-univalent Function Class $\Sigma $. Math. Sci. Appl. E-Notes. March 2020;8(1):134-141. doi:10.36753/mathenot.650271
Chicago 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 8, no. 1 (March 2020): 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 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, 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 2020), 134-141. https://doi.org/10.36753/mathenot.650271.
JAMA 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, 2020, pp. 134-41, doi:10.36753/mathenot.650271.
Vancouver 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):134-41.

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