Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions linked with Horadam Polynomials
Abstract
In this work, we investigate some subclasses of bi-univalent and regular functions associated with Horadam polynomials in the open unit disk $\mathfrak{U}=\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. For functions that belong to these subclasses, we find bounds on their initial coefficients. The functional problem of Fekete-Szegö is also examined. Along with presenting some new results, we also talk about pertinent connections to earlier findings.
References
Abirami, C., Magesh, N., Yamini, J., & Gatti, N. B. (2020). Horadam polynomial coefficient estimates for the classes of A-bi-starlike and bi-Bazilevic function. Journal of Analysis, 28(4), 951-960. https://doi.org/10.1007/541478-020-00224-2
Amourah, A., Frasin, B. A., Swamy, S. R., & Sailaja, Y. (2022). Coefficient bounds for Al-Oboudi type bi-univalent functions connected with a modified sigmoid activation function and k-Fibonacci numbers. Journal of Mathematical Computer Science, 27, 105-117. https://doi.org/10.22436/jmcs.027.02.02
Brannan, D. A., & Clunie, J. G. (1979). Aspects of contemporary complex analysis. Proceedings of the NATO Advanced study institute held at University of Durhary. New York: Academic Press.
Brannan, D. A., & Taha, T. S. (1986). On some classes of bi-univalent functions. Studia Universitatis Babes-Bolyai Mathematica, 31 (2), 70-77.
Deniz, E. (2013). Certain subclasses of bi-univalent functions satisfying subordinate conditions. Journal of Classical Analysis, 2(1), 49-60. https://doi.org/10.7153/jca-02-05
Duren, P. L. (1983). Univalent functions. Grundlehren der Mathematischen Wissenschaften, Band 259. Springer-Verlag.
El-Deeb, S. M., Bulboacă, T., & El-Matary, B. M. (2020). Maclaurin coefficient estimates of bi-univalent functions connected with the q-derivative. Mathematics, 8, 418. https://doi.org/10.3390/math8030418
Fekete, M., & Szegő, G. (1933). Eine Bemerkung Über Ungerade Schlichte Funktionen. Journal of the London Mathematical Society, 89, 85-89. https://doi.org/10.1112/jlms/s1-8.2.85
Frasin, B. A. (2014). Coefficient bounds for certain classes of bi-univalent functions. Hacet. Journal of Mathematics and Statistics, 43(3), 383-389.
Frasin, B. A., & Aouf, M. K. (2011). New subclasses of bi-univalent functions. Applied Mathematics, 24, 1569-1573. https://doi.org/10.1016/j.aml.2011.03.048
Frasin, B. A., Swamy, S. R., & Aldawish, A. (2021). A comprehensive family of bi-univalent functions defined by k-Fibonacci numbers. Journal of Function Spaces, 2021, Article ID 4249509, 8 pages. https://doi.org/10.1155/2021/4249509
Hörçum, T., & Koçer, E. G. (2009). On some properties of Horadam polynomials. International Mathematical Forum, 4, 1243-1252.
Horadam, A. F., & Mahon, J. M. (1985). Pell and Pell-Lucas polynomials. Fibonacci Quarterly, 23, 7-20.
Khan, B., Srivastava, H. M., Tahir, M., Darus, M., Ahmed, Q. Z., & Khan, N. (2020). Applications of a certain q-integral operator to the subclasses of analytic and bi-univalent functions. AIMS Mathematics, 6(1), 1024-1039.
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
Magesh, N., Yamini, J., & Abhirami, C. (2018). Initial bounds for certain classes of bi-univalent functions defined by Horadam polynomials. arXiv: 1812.04464v1 [math.cv].
Orhan, H., Mamatha, P. K., Swamy, S. R., Magesh, N., & Yamini, J. (2021). Certain classes of bi-univalent functions associated with the Horadam polynomials. Acta Universitatis Sapientiae, Mathematica, 13(1), 258-272. https://doi.org/10.2478/ausm-2021-0015
Shammaky, A. E., Frasin, B. A., & Swamy, S. R. (2022). Fekete-Szegö inequality for bi-univalent functions subordinate to Horadam polynomials. Journal of Function Spaces, 2022, Article ID 9422945, 7 pages. https://doi.org/10.1155/2022/9422945
Srivastava, H. M. (2020). Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis. Iranian Journal of Science and Technology, Transaction A, Science, 44, 327-344. https://doi.org/10.1007/s40995-019-00815-0
Srivastava, H. M., Altınkaya, Ş., & Yalçın, S. (2019). Certain subclasses of bi-univalent functions associated with the Horadam polynomials. Iranian Journal of Science and Technology, Transaction A, Science, 43, 1873-1879. https://doi.org/10.1007/s40995-018-0647-0
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
Srivastava, H. M., Wanas, A. K., & Tan, R. (2021). Applications of the q-Srivastava-Attiya operator involving a family of bi-univalent functions associated with Horadam polynomials. Symmetry, 13(7), 1230. https://doi.org/10.3390/sym13071230
Swamy, S. R. (2021). Coefficient bounds for Al-Oboudi type bi-univalent functions based on a modified sigmoid activation function and Horadam polynomials. Earthline Journal of Mathematics Sciences, 7(2), 251-270. https://doi.org/10.34198/ejms.7221.251270
Swamy, S. R., & Nirmala, J. (2021). Some special families of holomorphic and Al-Oboudi type bi-univalent functions associated with (m, n)-Lucas polynomials involving modified sigmoid activation function. South East Asian Journal of Mathematics and Mathematical Sciences, 17(1), 1-16.
Swamy, S. R., & Sailaja, Y. (2020). Horadam polynomial coefficient estimates for two families of holomorphic and bi-univalent functions. International Journal of Mathematical Trends and Technology, 66(8), 131-138. https://doi.org/10.14445/22315373/IJMTT-V6618P514
Swamy, S. R., & Wanas, A. K. (2022). A comprehensive family of bi-univalent functions defined by (m,n)-Lucas polynomials. Bol. Soc. Mat. Mex., 28(34), 10 pages. https://doi.org/10.1007/s40590-022-00411-0
Swamy, S. R., & Yalçın, S. (2022). Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials. Problems, Analysis and Issues in Analysis, 11 (1), 133-144. https://doi.org/10.15393/j3.art.2022.10351
Tan, D. L. (1984). Coefficient estimates for bi-univalent functions. Chinese Annals of Mathematics, Series A, 5, 559-568.
Tang, H., Deng, G., & Li, S. (2013). Coefficient estimates for new subclasses of Ma-Minda bi-univalent functions. Journal of Inequalities and Applications, 2013, Art. 317, 10 pages. https://doi.org/10.1186/1029-242X-2013-317
Wanas, A. K., Swamy, S. R., Tang, H., Shaba, T. G., Nirmala, J., & Ibrahim, I. O. (2021). A comprehensive family of bi-univalent functions linked with Gegenbauer polynomials. Turkish Journal of Inequalities, 5(2), 61-69.
Wanas, A. K., & Lupas, A. A. (2019). Applications of Horadam polynomials on Bazilevic bi-univalent function satisfying subordinate conditions. IOP Conference Series: Journal of Physics: Conference Series, 1294, 032003. https://doi.org/10.1088/1742-6596/1294/3/032003
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