Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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NEW SUBCLASS OF MEROMORPHIC MULTIVALENT FUNCTIONS ASSOCIATED WITH HYPERGEOMETRIC FUNCTION

  • Khadr, Mohamed A. (Department of Mathematics, College of Computer Science and Mathematics University of Mosul) ;
  • Ali, Ahmed M. (Department of Mathematics, College of Computer Science and Mathematics University of Mosul) ;
  • Ghanim, F. (Department of Mathematics, College of Sciences University of Sharjah)
  • Received : 2020.12.10
  • Accepted : 2021.03.11
  • Published : 2021.09.15
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Abstract

As hypergeometric meromorphic multivalent functions of the form $$L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)=\frac{1}{{\zeta}^{\rho}}+{\sum\limits_{{\kappa}=0}^{\infty}}{\frac{(\varpi)_{{\kappa}+2}}{{(\sigma)_{{\kappa}+2}}}}\;{\cdot}\;{\frac{({\rho}-({\kappa}+2{\rho})t)}{{\rho}}}{\alpha}_{\kappa}+_{\rho}{\zeta}^{{\kappa}+{\rho}}$$ contains a new subclass in the punctured unit disk ${\sum_{{\varpi},{\sigma}}^{S,D}}(t,{\kappa},{\rho})$ for -1 ≤ D < S ≤ 1, this paper aims to determine sufficient conditions, distortion properties and radii of starlikeness and convexity for functions in the subclass $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

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Acknowledgement

This paper was supported by the College of Computer Sciences and Mathematics, University of Mosul, Republic of Iraq and College of Sciences, University of Sharjah, UAE.

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