Coefficient Problems on Bi-Univalent Functions With (p,q)-Gegenbauer Polynomials

Authors

DOI:

https://doi.org/10.26713/cma.v15i3.2742

Keywords:

Taylor-Maclaurin series, Starlike functions, Convex functions, Biunivalent functions, Coefficient bounds, Fekete-Szegö inequality, (p, q)-Gegenbauer polynomials

Abstract

In this paper, our main aim is to study a new subclass of bi-univalent functions and to obtain initial coefficient bounds of starlike and convex bi-univalent functions involving (p,q)-Gegenbauer polynomials. Also, we aim at obtaining sharp bound for Fekete-Szegö functional.

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References

A.G. Alamoush, A subclass of pseudo-type meromorphic bi-univalent functions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69(2) (2020), 1025 – 1032, DOI: 10.31801/cfsuasmas.650840.

D.A. Brannan and J.G. Clunie, Aspects of Contemporary Complex Analysis, Academic Press, New York — London, pp. 572 (1979).

D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Mathematical Analysis and its Applications (Proceedings of the International Conference on Mathematical Analysis and its Applications, Kuwait, 1985) (1988), 53 – 60, DOI: 10.1016/B978-0-08-031636-9.50012-7.

R. Chakrabarti and R. Jagannathan, A (p, q)-oscillator realization of two-parameter quantum algebras, Journal of Physics A: Mathematical and General 24(13) (1991), L711, DOI: 10.1088/0305-4470/24/13/002.

L. de Branges, A proof of the Bieberbach conjecture, Acta Mathematica 154 (1985), 137 – 152, DOI: 10.1007/BF02392821.

P.L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften 259 (1983), 382.

B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Applied Mathematics Letters 24(9) (2011), 1569 – 1573, DOI: 10.1016/j.aml.2011.03.048.

K. Kiepiela, I. Naraniecka and J. Szynal, The Gegenbauer polynomials and typically real functions, Journal of Computational and Applied Mathematics 153 (2003), 273 – 282, DOI: 10.1016/S0377-0427(02)00642-8.

M. Lewin, On a coefficient problem for bi-univalent functions, Proceedings of the American Mathematical Society 18 (1967), 63 – 68, DOI: 10.1090/S0002-9939-1967-0206255-1.

N. Magesh and S. Bulut, Chebyshev polynomial coefficient estimates for a class of analytic biunivalent functions related to pseudo-starlike functions, Afrika Matematika 29 (2018), 203 – 209, DOI: 10.1007/s13370-017-0535-3.

N. Magesh, A. Motamednezhad and S. Salehian, Certain subclass of bi-univalent functions associated with the Chebyshev polynomials based on q-derivative and symmetric q-derivative, Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science 13(62) (2020), 163 – 176, DOI: 10.31926/but.mif.2020.13.62.2.18.

N. Magesh, C. Abirami and S. Altınkaya, Initial bounds for certain classes of bi-univalent functions defined by the (p, q)-Lucas polynomials, TWMS Journal of Applied and Engineering Mathematics 11(1) (2021), 282 – 288, URL: https://jaem.isikun.edu.tr/web/index.php/archive/110-vol11-no1/684-initial-bounds-for-certain-classes-of-bi-univalent-functions-defined-by-the-p-qlucas-polynomials.

S. Miller and P. Mocanu, Differential Subordination: Theory and Applications, 1st edition, CRC Press, Boca Raton, 480 pages (2000), DOI: 10.1201/9781482289817.

H. Orhan, N. Magesh and V. Balaji, Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials, Asian-European Journal of Mathematics, 12(02) (2019), 1950017, DOI: 10.1142/S1793557119500177.

H. Orhan, P.K. Mamatha, S.R. Swamy, N. Magesh and J. Yamini, Certain classes of bi-univalent functions associated with the Horadam polynomials, Acta Universitatis Sapientiae Mathematica 13(1) (2021), 258 – 272, DOI: 10.2478/ausm-2021-0015.

Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Göttingen, (1975).

H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Applied Mathematics Letters 23 (2010), 1188 – 1192, DOI: 10.1016/j.aml.2010.05.009.

T.S. Taha, Topics in Univalent Function Theory, Ph.D. Thesis, University of London, London (1981).

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Published

30-11-2024

How to Cite

Raju, R. G., Salestina, M. R., & Gatti, N. B. (2024). Coefficient Problems on Bi-Univalent Functions With (p,q)-Gegenbauer Polynomials. Communications in Mathematics and Applications, 15(3), 1011–1019. https://doi.org/10.26713/cma.v15i3.2742

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Research Article