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Coefficient bounds for bi-univalent analytic functions associated with Hohlov operator

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In the present paper, the authors introduce and investigate two newsubclasses of the function class ∑ of bi-univalent analytic functions in the openunit disk Δ associated with Hohlov operator. The bounds on the coefficients|a2|, |a3| and |a4| for the functions in these new subclasses of ∑ are obtained. Relevant connection of the results presented here with those obtained in earlierwork are also pointed out.

Abstract

In the present paper, the authors introduce and investigate two newsubclasses of the function class ∑ of bi-univalent analytic functions in the openunit disk Δ associated with Hohlov operator. The bounds on the coefficients|a2|, |a3| and |a4| for the functions in these new subclasses of ∑ are obtained. Relevant connection of the results presented here with those obtained in earlierwork are also pointed out.

참고문헌 (11)

  1. D.A. Brannan, "Aspects of Contemporary Complex Analysis", Proceeding of the NATO Advanced study Institute held at the University of Durham (1979), Academic Press
  2. D.A. Brannan, "Coefficient estimates for a class of star-like functions", Canad. J. Math, 22, pp.476~485 (1970)
  3. D.A. Brannan, "On some classes of bi-univalent functions", KFAS Proceedings Series, 3, pp.70~77 (1988), Pergamon Press
  4. P.L. Duren, "Univalent Functions, In Grundlehren der Mathematischen Wissenschaften" (1983), Springer-Verlag
  5. B.A. Frasin, "New subclasses of bi-univalent functions", Appl. Math. Lett, 24, pp.1569~1973 (2011)
  6. Yu.E. Hohlov, "Operators and operations in the class of univalent functions", Izv. Vyss. Ucebn. Zaved. Matematika, 10, pp.83~89 (1978)
  7. M. Lewin, "On a coefficient problem for bi-univalent functions", Proc. Amer. Math. Soc, 18, pp.63~68 (1967)
  8. 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, pp.100~112 (1969)
  9. H.M. Srivastava, "Certain subclasses of analytic and bi-univalent functions", Appl. Math. Lett, 23, pp.1188~1192 (2010)
  10. T.S. Taha, "Topics in Univalent Function Theory", 박사, pp.1981
  11. Q.-H. Xu, "Coefficient estimates for a certain subclass of analytic and bi-univalent functions", Appl. Math. lett, 25, pp.990~994 (2012)

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