Abstract
In the present paper, we give sufficient conditions for a function f to be in the subclasses \( \sum S_{a,s}^*(A,\,B,\,\alpha ,\,\beta ) \) and \( \sum {\kappa _{a,\,s}}(A,\,B,\,\alpha ,\,\beta ) \) of the class Σ of meromorphic functions which are analytic in the punctured unit disk U*. We further investigate the ratio of a function related to the Hurwitz-Lerch zeta function and its sequence of partial sums.
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A. W. Goodman, Univalent Functions, Vol. I, Mariner Publishing Company, Tampa, Florida, 1983.
N. E. Cho and S. Owa, On partial sums of certain meromorphic functions, J. Inequal. Pure Appl. Math. 5 (2) (2004), Article 30, 1–7.
F. Ghanim, A study of a certain subclass of Hurwitz-Lerch zeta function related to a linear operator, Abstr. Appl. Anal. 2013 (2013), Article ID 763756, 1–7.
F. Ghanim and M. Darus, New result of analytic functions related to Hurwitz-Zeta function, The Sci. World J. 2013 (2013), Article ID 475643, 1–5.
F. Ghanim and M. Darus, Partial sums of certain new subclasses for meromorphic functions, Far East J. Math. Sci. 55 (2011), 181–195.
R. W. Ibrahim and M. Darus, Partial sums for certain classes of meromorphic functions, Tamkang J. Math. 41 (2010), 39–49.
S. Latha and L. Shivarudrappa, Partial sum of meromorphic functions, J. Inequal. Pure Appl. Math. 7 (4) (2006), Article 140, 1–8.
E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209 (1997), 221–227.
R. Singh and S. Singh, Convolution properties of a class of starlike fuctions, Proc. Amer. Math. Soc. 106 (1989), 145–152.
H. M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000), 77–84.
H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inform. Sci. 5 (2011), 390–444.
H. M. Srivastava and J. Choi, Series Associated with Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
H. M. Srivastava, S. Gaboury and F. Ghanim, Certain subclasses of meromorphically univalent functions defined by a linear operator associated with the λ-generalized Hurwitz-Lerch zeta function, Integral Transforms Spec. Funct. 26 (2015), 258–272.
H. M. Srivastava, S. Gaboury and F. Ghanim, Some further properties of a linear operator associated with the λ-generalized Hurwitz-Lerch zeta function related to the class of meromorphically univalent functions, Appl. Math. Comput. 259 (2015), 1019–1029.
H. M. Srivastava, S. Gaboury and F. Ghanim, A study of meromorphically univalent functions defined by a linear operator associated with the λ-generalized Hurwitz-Lerch zeta function, Preprint (2015), 1–12.
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwoord Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.
S.-M. Yuan, Z.-M. Liu and H. M. Srivastava, Some inclusion relationships and integral-preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators, J. Math. Anal. Appl. 337 (2008), 505–515.
Z.-G. Wang, H. M. Srivastava and S.-M. Yuan, Some basic properties of certain subclasses of meromorphically starlike functions, J. Inequal. Appl. 2014 (2014), Article ID 2014:29, 1–12.
W. Rogosinski and G. Szegö, Über die abschimlte von potenzreihen die in ernein kreise be schranket bleiben, Math. Zeitschr. 28 (1928), 73–94.
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2010 Mathematics Subject Classification. 30C45, 11M35, 30C10.
1 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada. E-Mail: harimsri@math.uvic.ca
2 Department of Mathematics and Computer Science, University of Québec at Chicoutimi, Chicoutimi, Québec G7H 2B1, Canada. E-Mail: s1gabour@uqac.ca
3 Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates. E-Mail: fgahmed@sharjah.ac.ae
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Srivastava, H., Gaboury, S. & Ghanim, F. Partial Sums of Certain Classes of Meromorphic Functions Related to the Hurwitz-Lerch Zeta Function. Moroc J Pure Appl Anal 1, 3 (2015). https://doi.org/10.7603/s40956-015-0003-8
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DOI: https://doi.org/10.7603/s40956-015-0003-8