Nonlinear Functional Analysis and Applications

The Basic Sciences Research Institute, Kyungnam University (경남대학교 기초과학연구소)
권호 표지
DOI QR코드

DOI QR Code

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
Download PDF
⟨ Previous Next ⟩

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 $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

Keywords

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.

References

  1. M. Albehbah and M. Darus, New subclass of multivalent hypergeometric meromorphic functions, Kragujevac J. Math., 42(1) (2018), 83-95. https://doi.org/10.5937/KgJMath1801083A
  2. H.F. Al-Janaby, F. Ghanim and M.Z. Ahmad, Harmonic multivalent functions associated with an extended generalized linear operator of Noor-type, Nonlinear Funct. Anal. Appl., 24(2) (2019), 269-292.
  3. H.F. Al-Janaby and F. Ghanim, A subclass of Noor-Type harmonic p-valent functions based on hypergeometric functions, Kragujevac J. Math., 45(4) (2021), 499-519. https://doi.org/10.46793/KgJMat2104.499J
  4. M.K. Aouf, New criteria for multivalent meromorphic starlike functions of order α, Proc. Japan Acad. Ser. A. Math. Sci., 69 (1993), 66-70.
  5. N.E. Cho and I.H. Kim, Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 187 (2007), 115-121. https://doi.org/10.1016/j.amc.2006.08.109
  6. J. Dziok and H.M. Srivastava, Certain subclasses of analytic functions associated with the Generalized hypergeometric function, Integral Trans. Spec. Funct., 14(1) (2003), 7-18. https://doi.org/10.1080/10652460304543
  7. R.M. El-Ashwah, Some properties of certain subclasses of meromorphically multivalent functions, Appl. Math. and Comput., 204 (2008), 824-832. https://doi.org/10.1016/j.amc.2008.07.032
  8. F. Ghanim, M. Darus and S. Sivasubramanian, New subclass of hypergeometric meromorphic functions, Far East J. Math. Sci., 34(2) (2009), 245-256.
  9. F. Ghanim and M. Darus, New subclass of multivalent hypergeometric meromorphic functions, Int. J. Pure Appl. Math., 61(3) (2010), 269-280.
  10. F. Ghanim and M. Darus, Some properties of certain subclass of meromorphically multivalent functions defined by linear operator, J. Math. Stattis., 6 (1) (2010), 34-41. https://doi.org/10.3844/jmssp.2010.34.41
  11. F. Ghanim and Hiba F. Al-Janay, A certain subclass of univalent meromorphic functions defined by a linear operator associated with the Hurwitz-Lerch Zeta Function, Rad HAZU Matematicke Znanosti (Rad Hrvat. Akad. Znan. Umjet. Mat. Znan.), 23 (2019), 71-83.
  12. S.B. Joshi and H.M. Srivastava, A certain family of meromorphically multivalent functions, Comput. Math. Appl., 38 (3-4) (1999), 201-211. https://doi.org/10.1016/S0898-1221(99)00194-7
  13. S.R. Kulkarni, U.H. Naik and H.M. Srivastava, A certain class of meromorphically pvalent quasi-convex functions, Pan Amer. Math. J., 8(1) (1998), 57-64.
  14. J.L. Liu, A linear operator and its applications on meromorphic p-valent functions, Bull. Inst. Math. Acad. Sin., 31(1) (2003), 23-32.
  15. J.L. Liu and H.M. Srivastava, A linear operator and associated families of meromorphically multivalent functions, J. Math. Anal. Appl., 259 (2001), 566-581. https://doi.org/10.1006/jmaa.2000.7430
  16. A.K. Mishra, T. Panigrahi and R.K. Mishra, Subordination and inclusion theorems for subclasses of meromorphic functions with applications to electromagnetic cloaking, Math. Comput. Model., 57 (2013), 945-962. https://doi.org/10.1016/j.mcm.2012.10.005
  17. M.L. Mogra, Meromorphic multivalent functions with positive coefficients I, Math. Japon., 35 (1990), 1-11.
  18. S. Owa, H.E. Darwish and M.K. Aouf, Meromorphic multivalent functions with positive and fixed second coefficients, Math. Japan, 46 (1997), 231-236.
  19. H.M. Srivastava and S. Owa, Editors, Current topics in analytic function theory, World Sci. Sing., 1992.
  20. B.A. Uralegaddi and C. Somanatha, Certain classes of meromorphic multivalent functions, Tamkang J. Math., 23 (1992), 223-231. https://doi.org/10.5556/j.tkjm.23.1992.4545
  21. D.G. Yang, On new subclasses of meromorphic p-valent functions, J. Math. Res. Exp., 15 (1995), 7-13.