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Coefficient problem for alpha-convex univalent functions

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Abstract

Let {ie205-01} be an α-convex univalent function in the open unit disk. In this paper we shall determine sharp bounds for the moduli ¦a n} of the coefficients.

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References

  1. 1.

    Bazilevič, I. E., On a case of integrability in quadrature of the Löwner-Kufarev equation. Mat. Sb. (79), 37, 471–476 (1955).

  2. 2.

    Goodman, A. W., Coefficients for the area theorem. Proc. Amer. Math. Soc. 33, 438–444 (1972).

  3. 3.

    Kulshrestha, P. K., Coefficient problems for a class of Mocanu-Bazilevič functions.

  4. 4.

    Kulshrestha, P. K., Coefficients for alpha-convex univalent functions. Bull. Amer. Math. Soc. (to appear).

  5. 5.

    Mocanu, P. T., Une propriété de convexité généralisée dans la théorie de la représentation conforme. Mathematica (Cluj) (34), 11, 127–133 (1969).

  6. 6.

    Miller, S. S., Distortion properties of alpha-starlike functions. Proc. Amer. Math. Soc. 38, 311–318 (1973).

  7. 7.

    Pflatzgraft, J. A., On the Marx conjecture for a class of close-to-convex functions. Michigan Math. J. 18, 275–278 (1971).

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Communicated by M. M. Schiffer

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Kulshrestha, P.K. Coefficient problem for alpha-convex univalent functions. Arch. Rational Mech. Anal. 54, 205–211 (1974). https://doi.org/10.1007/BF00250787

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Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Unit Disk
  • Electromagnetism