Taiwanese Journal of Mathematics

A CLASS OF MEROMORPHIC MULTIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS

M. K. Aouf

Full-text: Open access

Abstract

In this paper, we introduce a class $F_{\lambda ,p}^{n}(\alpha ,\beta ,\gamma )$ of meromorphic multivalent functions in $U^{*}=\{z:0\lt |z|\lt 1\}$ by using a differential operator $D_{\lambda ,p}^{n}f(z)$. We obtain coefficient estimates, distortion theorem, radius of convexity, closure theorems and integral transforms for the class $F_{\lambda ,p}^{n}(\alpha ,\beta ,\gamma )$. Several results involving the Hadamard products of functions belonging to the class $F_{\lambda ,p}^{n}(\alpha ,\beta ,\gamma )$ are also derived.

Article information

Source
Taiwanese J. Math., Volume 12, Number 9 (2008), 2517-2533.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405193

Digital Object Identifier
doi:10.11650/twjm/1500405193

Mathematical Reviews number (MathSciNet)
MR2479069

Zentralblatt MATH identifier
1170.30301

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Keywords
analytic meromorphic positive coefficients

Citation

Aouf, M. K. A CLASS OF MEROMORPHIC MULTIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS. Taiwanese J. Math. 12 (2008), no. 9, 2517--2533. doi:10.11650/twjm/1500405193. https://projecteuclid.org/euclid.twjm/1500405193


Export citation

References

  • M. K. Aouf, A generalization of meromorphic multivalent functions with positive coefficients, Math. Japon., 35 (1990), 609-614.
  • M. K. Aouf, On a class of meromorphic multivalent functions with positive coefficients, Math. Japon., 35 (1990), 603-608.
  • M. K. Aouf, H. M. Hossen and H. E. Elattar, A certain class of meromorphic multivalent functions with positive and fixed second coefficients, Punjab Univ. J. Math., 333 (2000), 115-124.
  • N. E. Cho, S. H. Lee and S. Owa, A class of meromorphic univalent functions with positive coefficients, Kobe J. Math., 4 (1987), 43-50.
  • S. B. Joshi and M. K. Aouf, Meromorphic multivalent functions with positive and fixed second coefficients, Kyungpook Math. J., 35 (1995), 163-169.
  • S. B. Joshi and H. M. Srivastava, A certain family of meromorphically multivalent functions, Comput. Math. Appl., 38(3-4) (1999), 201-211.
  • J. -L. Liu, Properties of some families of meromorphic p-valent functions, Math. Japon., 52 (2000), 425-434.
  • J. -L. Liu and H. M. Srivastava, A linear operator and associated families of mermorphically multivalent function, J. Math. Anal. Appl., 259 (2001), 566-581.
  • M. L. Mogra, Meromorphic multivalent functions with positive coefficients. I, Math. Japon., 35(1) (1990), 1-11.
  • M. L. Mogra, Meromorphic multivalent functions with positive coefficients. II, Math. Japon., 35(6) (1990), 1089-1098.
  • S. Owa, H. E. Darwish and M. K. Aouf, Meromorphic multivalent functions with positive and fixed second coefficients, Math. Japon., 46(2) (1997), 231-236.
  • R. K. Raina and H. M. Srivastava, A new class of meromorphically multivalent functions with applications to generalized hypergeometric functions, Math. Comput. Modelling, 43 (2006), 350-356.
  • A. Schild and H. Silverman, Convolution of univalent functions with negative coefficients, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 29 (1975), 99-107.
  • H. M. Srivastava, H. M. Hossen and M. K. Aouf, A unified presentation of some classes of meromorphically multivalent functions, Comput. Math. Appl., 38 (1999), 63-70.
  • B. A. Uralegaddi and M. D. Ganigi, Meromorphic multivalent functions with positive coefficients, Nepali Sci. Rep., 11 (1986), 95-102.
  • D. -G. Yang, On new subclasses of meromorphic p-valent functions, J. Math. Res. Exposition, 15 (1995), 7-13.