Estimates on initial coefficients of certain subclasses of bi-univalent functions associated with quasi-subordination
DOI:
https://doi.org/10.14419/gjma.v5i1.6959الكلمات المفتاحية:
Analytic function، Bi-univalent function، Quasi-subordination، Subordination، Univalent function.الملخص
v In the present investigation we introduce some subclasses of the function class ∑ of bi-univalent functions defined in the open unit disk U, which are associated with the quasi-subordination. We obtain the estimates on initial coefficients |a2| and |a3| for the functions in these subclasses. Also several related subclasses are considered and connection with some known results are established.
المراجع
[1] R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, “Coefficient estimates for bi-univalent Ma-Minda starlike and convex functionsâ€, Appl. Math. Lett., 25, (2012), 344–351.
[2] D. A. Brannan and J. G. Clunie (Eds.), Aspects of Contemporary Complex Analysis, (Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1-20, 1979), Academic Press, New York and London, (1980).
[3] D. A. Brannan and T. S. Taha, “On some classes of bi-univalent functionsâ€, Studia Univ. Babes-Bolyai Math, 31, (2), (1986), 70–77.
[4] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, (1983).
[5] B. A. Frasin and M. K. Aouf, “New subclasses of bi-univalent functionsâ€, Appl. Math. Lett., 24, (2011), 1569–1573.
[6] F. R. Keogh and E. P. Merkes, “A coefficient inequality for certain classes of analytic functionsâ€, Proc. Amer. Math. Soc., 20, (1969), 8–12.
[7] S. S. Kumar, V. Kumar and V. Ravichandran, “Estimates for the initial coefficients of bi-univalent functionsâ€, Tamsui Oxf. J. Inf. and Math. Sci., 29, (4), (2013), 487–504.
[8] M. Lewin, “On a coefficient problem for bi-univalent functionsâ€, Proc. Amer. Math. Soc., 18, (1967), 63–68.
[9] W. C. Ma and D. Minda, “A unified treatment of some special classes of univalent functionsâ€, Proceedings of the Conference on Complex Analysis, Tianjin, (1992), 157–169.
[10] M. H. Mohd and M. Darus, “Fekete Szego problems for Quasisubordination classesâ€, Abst. Appl. Anal., Article ID 192956, (2012), 1–14.
[11] E. Netanyahu, “The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1â€, Arch. Rational Mech. Anal., 32, 1969), 100–112.
[12] Ch. Pommerenke, Univalent functions, Vandenhoeck and Rupercht, Gottingen, (1975).
[13] V. Ravichandran, Y. Polatoglu, M. Bolcal and A. Sen, “Certain subclasses of starlike and convex functions of complex orderâ€, Hacet. J. Math. Stat., 34, (2005), 9–15.
[14] F. Y. Ren, S. Owa and S. Fukui, “Some inequalities on quasisubordinate functionsâ€, Bull. Aust. Math. Soc., 43, (2), (1991), 317–324.
[15] M. S. Robertson, “Quasi-subordination and coefficient conjectureâ€, Bull. Amer. Math. Soc., 76, (1970), 1–9.
[16] H. M. Srivastava, A. K. Mishra and P. Gochhayat, “Certain subclasses of analytic and bi-univalent functionsâ€, Appl. Math. Lett., 23, (2010), 1188–1192.
[17] T. S. Taha, Topics in Univalent Function Theory, Ph. D. Thesis, University of London, London, (1981).
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