Research Article Open Access

A Certain Subclass of Meromorphically Multivalent Analytic Functions with Negative Coefficients

M.Z. Ahmad1, Hiba F. Al-Janaby2 and Rabha W. Ibrahim3
  • 1 Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau Perlis, Malaysia
  • 2 Department of Mathematics, College of Science, University of Baghdad, Iraq
  • 3 Faculty of Computer Science and IT, University Malaya, 50603 Kuala Lumpur, Malaysia

Abstract

The paper aims to introduce a certain subclass S*g(A,B,α,p,j) of the class Σ*(p) of meromorphically multivalent functions with negative coefficients, defined by using the definitions of Hadamard product and subordination for two functions belong to the class Σ*(p). We first investigate the geometric characterization property, giving the coefficient estimates for functions in the class S*g(A,B,α,p,j). We also obtain the distortion theorem, radii of meromorphically p-valent starlikeness and convexity of order (0≤γ<p), neighborhood property, partial sums, convolution properties as well as integral operator and integral representation.

American Journal of Applied Sciences
Volume 12 No. 9, 2015, 606-615

DOI: https://doi.org/10.3844/ajassp.2015.606.615

Submitted On: 4 May 2015 Published On: 2 October 2015

How to Cite: Ahmad, M., Al-Janaby, H. F. & Ibrahim, R. W. (2015). A Certain Subclass of Meromorphically Multivalent Analytic Functions with Negative Coefficients. American Journal of Applied Sciences, 12(9), 606-615. https://doi.org/10.3844/ajassp.2015.606.615

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Keywords

  • Meromorphic Function
  • Multivalent Function
  • Subordination
  • Hadamard Product