Coefficient Estimates for Two New Subclasses of Bi-univalent Functions Involving Laguerre Polynomials
Abstract
In this paper, we introduce two new subclasses of regular and bi-univalent functions using Laguerre polynomials. Then, we define some upper limits for the Taylor Maclaurin coefficients. In addition, the Fekete-Szegö problem for the functions of the new subclasses. Finally, we provide some corollaries for certain values of parameters.
References
Amourah, A., Frasin, B. A., & Abdeljawad, T. (2021). Fekete-Szegö inequality for analytic and biunivalent functions subordinate to Gegenbauer polynomials. Journal of Function Spaces, 2021, Article ID 5574673. https://doi.org/10.1155/2021/5574673
Behera, A., & Panda, G. K. (1999). On the square roots of triangular numbers. Fibonacci Quarterly, 37, 98-105. https://doi.org/10.1080/00150517.1999.12428864
Brannan, D., & Clunie, J. (1980). Aspects of contemporary complex analysis. Academic Press.
Brannan, D., & Taha, T. S. (1988). On some classes of bi-univalent functions. In Proceedings of the International Conference on Mathematical Analysis and its Applications (pp. 53-60). https://doi.org/10.1016/B978-0-08-031636-9.50012-7
Çağlar, M. (2019). Chebyshev polynomial coefficient bounds for a subclass of bi-univalent functions. Comptes Rendus de l'Académie Bulgare des Sciences, 72, 1608-1615. https://doi.org/10.7546/CRABS.2019.12.02
Çağlar, M., Orhan, H., & Yağmur, N. (2013). Coefficient bounds for new subclasses of bi-univalent functions. Filomat, 27, 1165-1171. https://doi.org/10.2298/FIL1307165C
Cotîrlă, L.-I., & Wanas, A. K. (2023). Applications of Laguerre polynomials for Bazilevič and $theta$-pseudo-starlike bi-univalent functions associated with Sakaguchi-type functions. Symmetry, 15, Article ID 406, 1-8. https://doi.org/10.3390/sym15020406
Duren, P. L. (1983). Univalent functions. Grundlehren der Mathematischen Wissenschaften (Vol. 259). Springer-Verlag.
Elumalai, M. (2024). Bi-univalent functions of complex order defined by Hohlov operator associated with (P,Q)-Lucas polynomial. Sahand Communications in Mathematical Analysis, 21(1), 273-289.
Frasin, B. A., & Aouf, M. K. (2011). New subclasses of bi-univalent functions. Applied Mathematics Letters, 24, 1569-1573. https://doi.org/10.1016/j.aml.2011.03.048
Lewin, M. (1967). On a coefficient problem for bi-univalent functions. Proceedings of the American Mathematical Society, 18, 63-68. https://doi.org/10.1090/S0002-9939-1967-0206255-1
Miller, S. S., & Mocanu, P. T. (2000). Differential subordinations. Monographs and Textbooks in Pure and Applied Mathematics (Vol. 225). Marcel Dekker, Inc. https://doi.org/10.1201/9781482289817
Srivastava, H. M., Mishra, A. K., & Gochhayat, P. (2010). Certain subclasses of analytic and bi-univalent functions. Applied Mathematics Letters, 23, 1188-1192. https://doi.org/10.1016/j.aml.2010.05.009
Toklu, E., Aktas, I., & Sagsöz, F. (2019). On new subclasses of bi-univalent functions defined by generalized Salagean differential operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 776-783. https://doi.org/10.31801/cfsuasmas.475818
Wanas, A. K., & Lupaş, A. A. (2022). Applications of Laguerre polynomials on a new family of bi-prestarlike functions. Symmetry, 14, Article 645, 1-10. https://doi.org/10.3390/sym14040645
Wanas, A. K., & Swamy, S. R. (2023). Applications of the second kind Chebyshev polynomials of bi-starlike and bi-convex $lambda$-pseudo functions associated with Sakaguchi type functions. Earthline Journal of Mathematical Sciences, 13(2), 497-507. https://doi.org/10.34198/ejms.13223.497507
Wanas, A. K., Wanas, E. K., Catas, A., & Abdalla, M. (2024). Applications of (M,N)-Lucas polynomials for a certain family of bi-univalent functions associating $lambda$-pseudo-starlike functions with Sakaguchi type functions. Earthline Journal of Mathematical Sciences, 15(1), 1-10. https://doi.org/10.34198/ejms.15125.001010
Xu, Q. H., Xiao, H. G., & Srivastava, H. M. (2012). A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems. Applied Mathematics and Computation, 218(23), 11461-11465. https://doi.org/10.1016/j.amc.2012.05.034
Yilmaz, N., & Aktas, I. (2022). On some new subclasses of bi-univalent functions defined by generalized bivariate Fibonacci polynomial. Afrika Matematika, 33(2), Article 59. https://doi.org/10.1007/s13370-022-00993-y
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