An Application of generalized Fibonacci-like polynomial on New Subfamilies of Regular and Bi-univalent Functions
Keywords:
Regular functions, Bi-univalent functions, Generalized Bivariate FibonacciLike polynomials, Horadam polynomial, Chebyshev polynomials, subordinationAbstract
The present paper introduces the novel subfamilies of regular and bi-univalent functions Σ. The prominent group of Fibonacci polynomial ˜Vn(x, y) is utilized with subordination between regular functions in order to shape these subfamilies. In addition we derive coefficients inequalities for functions belonging to these subfamilies. Various results are exposed as separate cases of the current conclusions.
References
Koshy, T.(2001), Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Incorparation.
Panwar, y.K. and Singh, M. (2014), Generalized bivariate Fibonacci-like polynomials, Internat. J. Pure Math., 1, 8–13.
Duren, P.L. (1983), Univalent Functions, Grundlehren der Mathema- tischen Wissenschaften, Springer, New york, Ny, USA.
Lewin, M. (1967), On a coefficient problem for bi-univalent functions, Proceedings of the American Mathematical Society, 18, 63-68.
Brannan, D. and Clunie, J. (1980), Aspects of contemporary complex analysis, Academic Press.
Netanyahu, E. (1969), The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in —z— ¡ 1, Arch. Ration. Mech. Anal., 32, 100–112.
Alamoush, A.G. (2020), On a subclass of bi-univalent functions associated to Horadam polynomials, Internat. J. Open Problems in Complex Analy., 12, 58–65.
Saloomi, M.H., Abd, E.H., and Qahtan, G.A. (2021), Coefficient bounds for biconvex and bistarlike functions associated by quasi-subordination, Journal of Interdisciplinary Mathematics Vol. 24, No. 3, pp. 753–764
Aldawish, I., Al-Hawary, T. and Frasin, B.A. (2020), Subclasses of bi-univalent functions defined by Frasin differential operator, Mathematics, 8, 783.
Srivastava, H.M., Mishra, A.K., and Gochhayat, P. (2010), Certain subclasses of analytic and bi-univalent functions,” Applied Mathematics Letters, Vol. 23, No.10, 1188–1192
Juma, A.S., Saloomi, M.H. (2018), Coefficient bounds for certain subclass of analytic functions defined by quasi-subordination. Iraqi Journal of Science (eijs), 59(2C).(Iraq).
Duren, P.L. (1977), Subordination in complex analysis, Lecture Note in mathematics, Springer, Berlin. Germany, 599, 22-29.
Mishra, A.K., Panigrahi, T., Mishra, R.K. (2013), Subordination and inclusion theorems for subclasses of meromorphic functions with applications to electromagnetic cloaking, Math. Comput. Modelling 57,945-962.
Aktas, I., yilmaz, N. (2022). Initial Coefficients Estimate and Fekete-Szego¨ Problems for Two New Subclasses of Bi-Univalent Functions. Konuralp Journal of Mathematics. 10 (1) 138-148.
