Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Coefficient problem for alpha-convex univalent functions

  • 96 Accesses


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.

This is a preview of subscription content, log in to check access.


  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).

Download references

Author information

Additional information

Communicated by M. M. Schiffer

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation


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