Abstract and Applied Analysis

A Study of a Certain Subclass of Hurwitz-Lerch-Zeta Function Related to a Linear Operator

F. Ghanim

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Abstract

By using a linear operator with Hurwitz-Lerch-Zeta function, which is defined here by means of the Hadamard product (or convolution), the author investigates interesting properties of certain subclasses of meromorphically univalent functions in the punctured unit disk U * .

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 763756, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512064

Digital Object Identifier
doi:10.1155/2013/763756

Mathematical Reviews number (MathSciNet)
MR3108650

Zentralblatt MATH identifier
07095344

Citation

Ghanim, F. A Study of a Certain Subclass of Hurwitz-Lerch-Zeta Function Related to a Linear Operator. Abstr. Appl. Anal. 2013 (2013), Article ID 763756, 7 pages. doi:10.1155/2013/763756. https://projecteuclid.org/euclid.aaa/1393512064


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References

  • S. G. Krantz, “Meromorphic functions and singularities at infinity,” in Handbook of Complex Variables, pp. 63–68, Birkhuser, Boston, Mass, USA, 1999.
  • K. Knopp, “Meromorphic functions,” in Theory of Functions Parts I and II, Two Volumes Bound as One, Part II, chapter 2, pp. 34–57, Dover, New York, NY, USA, 1996.
  • H. M. Srivastava and A. A. Attiya, “An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination,” Integral Transforms and Special Functions, vol. 18, no. 3-4, pp. 207–216, 2007.
  • H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
  • H. M. Srivastava, D. Jankov, T. K. Pogány, and R. K. Saxena, “Two-sided inequalities for the extended Hurwitz-Lerch zeta function,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 516–522, 2011.
  • H. M. Srivastava, R. K. Saxena, T. K. Pogány, and R. Saxena, “Integral and computational representations of the extended Hurwitz-Lerch zeta function,” Integral Transforms and Special Functions, vol. 22, no. 7, pp. 487–506, 2011.
  • J. Dziok and H. M. Srivastava, “Certain subclasses of analytic functions associated with the generalized hypergeometric function,” Integral Transforms and Special Functions, vol. 14, no. 1, pp. 7–18, 2003.
  • F. Ghanim and M. Darus, “A new class of meromorphically analytic functions with applications to the generalized hypergeometric functions,” Abstract and Applied Analysis, vol. 2011, Article ID 159405, 10 pages, 2011.
  • F. Ghanim and M. Darus, “Some properties of certain subclass of meromorphically multivalent functions defined by linear operator,” Journal of Mathematics and Statistics, vol. 6, no. 1, pp. 34–41, 2010.
  • F. Ghanim and M. Darus, “New subclass of multivalent hypergeometric meromorphic functions,” International Journal of Pure and Applied Mathematics, vol. 61, no. 3, pp. 269–280, 2010.
  • J.-L. Liu and H. M. Srivastava, “Certain properties of the Dziok-Srivastava operator,” Applied Mathematics and Computation, vol. 159, no. 2, pp. 485–493, 2004.
  • J.-L. Liu and H. M. Srivastava, “Classes of meromorphically multivalent functions associated with the generalized hypergeometric function,” Mathematical and Computer Modelling, vol. 39, no. 1, pp. 21–34, 2004.
  • S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, vol. 225 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000.
  • S. Ponnusamy, “Differential subordination and Bazilevič functions,” Proceedings of the Indian Academy of Sciences. Mathematical Sciences, vol. 105, no. 2, pp. 169–186, 1995.
  • E. T. Whittaker and G. N. Watson, A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, Mass, USA, 4th edition, 1996.