A subclass with bi-univalence involving Horadam polynomials and its coefficient bounds

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-4073

Keywords:

Analytic functions, Bi-univalent functions, Horadam polynomials

Abstract

In this research contribution, we have constructed a subclass of analytic bi-univalent functions using Horadam polynomials. Bounds for certain coefficients and Fekete- Szegö inequalities have been estimated.

Author Biographies

Krishnan Muthunagai, Vellore Institute of Technology.

School of Advanced Sciences.

G. Saravanan, Patrician College of Arts and Science.

Dept. of Mathematics

S. Baskaran, Agurchand Manmull Jain College.

Dept. of Mathematics

References

A. Akgül and F. Sakar, ”A certain subclass of bi-univalent analytic functions introduced by means of the q-analogue of Noor integral operator and Horadam polynomials”, Turkish journal of mathematics, vol. 43, no. 5, pp. 2275-2286, 2019, doi: 10.3906/mat-1905-17

A. G. Alamoush, “Coefficient estimates for certain subclass of bi functions associated the Horadam polynomials”, 2018, arXiv: 1812.10589

D. Brannan and J. Clunie, Aspects of contemporary complex analysis. London: Academic Press, 1980.

T. Horzum and E. Gökçen Koçer, “On some properties of Horadam polynomials”, International mathematical forum, vol. 4, no. 25, pp. 1243-1252, 2009. [On line]. Available: https://bit.ly/2Sw3MGf

A. F. Horadam and J. M. Mahon, ”Pell and Pell-Lucas polynomials”, The Fibonacci quarterly, vol. 23, no. 1, pp. 7-20, 1985. [On line]. Available: https://bit.ly/2R137MV

A. Horadam, ”Jacobsthal representation polynomials”, The Fibonacci quarterly, vol. 35, no. 2, pp. 137-148, 1997. [On line]. Available: https://bit.ly/3ez7OWY

T. Koshy, Fibonacci and Lucas numbers with applications. New York, NY: Wiley, 2001, doi: 10.1002/9781118033067

M. Lewin, ”On a coefficient problem for bi-univalent functions”, Proceedings of the American Mathematical Society, vol. 18, no. 1, pp. 63-63, 1967, doi: 10.1090/s0002-9939-1967-0206255-1

A. Lupas, ”A Guide of Fibonacci and Lucas polynomials”, Octogon Mathematical Magazine, vol. 7, no. 1, pp. 2-12, 1999.

G. Saravanan and K. Muthunagai, “Estimation of upper bounds for initial coefficients and Fekete-Szegö inequality for a subclass of analytic bi-univalent functions”, in Applied mathematics and scientific computing, B. Rushi Kumar, R. Sivaraj, B. S. R. V. Prasad, M. Nalliah, and A. Subramanyam Reddy, Eds. Basel: Birkhäuser, 2019, pp. 57–65, doi: 10.1007/978-3-030-01123-9_7

G. Szegö, Orthogonal polynomials, 4th ed. Providence, RI: AMS, 1975.

R. Vijaya, T. Sudharsan and S. Sivasubramanian, ”Coefficient estimates for certain subclasses of biunivalent functions defined by convolution”, International journal of analysis, vol. 2016, Art. ID. 6958098, 2016, doi: 10.1155/2016/6958098

Q. Xu, Y. Gui, and H. Srivastava, ”Coefficient estimates for a certain subclass of analytic and bi-univalent functions”, Applied mathematics letters, vol. 25, no. 6, pp. 990-994, 2012, doi: 10.1016/j.aml.2011.11.013

S. Yalçin, K. Muthunagai and G. Saravanan, ”A subclass with bi-univalence involving (p,q)- Lucas polynomials and its coefficient bounds”, Boletín de la Sociedad Matemática Mexicana, vol. 26, pp. 1015–1022, doi: 10.1007/s40590-020-00294-z

Published

2021-05-12

How to Cite

[1]
K. Muthunagai, G. Saravanan, and S. Baskaran, “A subclass with bi-univalence involving Horadam polynomials and its coefficient bounds”, Proyecciones (Antofagasta, On line), vol. 40, no. 3, pp. 721-730, May 2021.

Issue

Section

Artículos