Abstract

In this study, by connecting these Lucas polynomials, subordination and differential operator, we introduce and investigate a new subclasses consisting of analytic and fold symmetric bi-univalent functions in the open unit disc . We obtain the coefficient bound for and also Fekete-Szegö inequalities for this new class.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 1
Year: 2023

DOI: 10.12732/ijam.v36i1.5

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References

1. [1] S. Altinkaya, S. Yal¸cin, Initial coefficient bounds for a general class of bi-univalent functions, Int. J. Anal., (2014), Article ID 867871, 4 pages.
2. [2] S¸. Altinkaya, S. Yal¸cin, Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Func. Spaces, (2015), Article ID 145242, 5 pages.
3. [3] D.A. Brannan, J. Clunie (Eds), Aspects of Contemporary Complex Analysis. Proc. of Instructional Conference Oorganized by the London Mathematical Society at the University of Durham, (1979) (a NATO Advanced Study Institute) (1980), 572 pages.
4. [4] D.A. Brannan, T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math., 31, No 2 (1986), 70–77.
5. [5] S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Math., 352, No 6 (2014), 479–484.
6. [6] P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY (1983).
7. [7] B.A. Frasin, M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24, No 9 (2011), 1569–1573.
8. [8] S.G. Hamidi, J. M. Jahangiri, Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Math., 352, No 1 (2014), 17– 20.
9. [9] J.M. Jahangiri, S.G. Hamidi, Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci., 2013 (2013), Article ID 190560, 4 pages.
10. [10] G. Lee, M. Asci, Some properties of the (p, q)-Fibonacci and (p, q)-Lucas polynomials, J. Appl. Math., 2012 (2012), Article ID 264842.
11. [11] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18, No 1 (1967), 63–68.
12. [12] W. Koepf, Coefficient of symmetric functions of bounded boundary rotations, Proc. Amer. Math. Soc., 105, No 2 (1989), 324–329.
13. [13] N. Magesh, J. Yamini, Coefficient bounds for a certain subclass of biunivalent functions, Int. Math. Forum, 8, No 27 (2013), 1337–1344.
14. [14] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1, Arch. Rational Mech. Anal., 32 (1969), 100–112.
15. [15] C. Pommerenke, Univalent Functions, Vandenhoeck und Ruprecht, G¨ottingen (1975).
16. [16] G.S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., 1013 (1983), 363–372, Springer-Verlag, Heidelberg and New York.
17. [17] H.M. Srivastava, A.K.Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, App. Math. Lett., 23, No 10 (2010), 1188–1192.
18. [18] H.M. Srivastava, S. Bulut, M. Caglar, N. Yagmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27, No 5 (2013), 831–842.
19. [19] H.M. Srivastava, S. Sivasubramanian, R. Sivakumar, Initial coefcient boundss for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J., 7, No 2 (2014), 1–10.
20. [20] Q.-H. Xu, Y.-C. Gui and H.M. Srivastava, Coeifficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25, No 6 (2012), 990–994.