Rad HAZU, Matematičke znanosti, Vol. 23 (2019), 71-83.

A CERTAIN SUBCLASS OF UNIVALENT MEROMORPHIC FUNCTIONS DEFINED BY A LINEAR OPERATOR ASSOCIATED WITH THE HURWITZ-LERCH ZETA FUNCTION

Firas Ghanim and Hiba F. Al-Janaby

Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
e-mail: fawzihiba@yahoo.com

Abstract.   In this paper, we study a linear operator related to Hurwitz-Lerch zeta function and hypergeometric function in the punctured unit disk. A certain subclass of meromorphically univalent functions associated with the above operator defined by the concept of subordination is also introduced, and its characteristic properties are studied.

2010 Mathematics Subject Classification.   30C45, 11M35, 30C10.

Key words and phrases.   Meromorphic functions, zeta functions, linear operators, Hadamard products.

DOI: https://doi.org/10.21857/ygjwrcjjxy

References:

1. K. R. Alhindi and M. Darus, A new class of meromorphic functions involving the polylogarithm function, J. Complex Anal. 2014 (2014), Art. ID 864805, 5 pp.
   MathSciNet     CrossRef

2. S. K. Bajpai, A note on a class of meromorphic univalent functions, Rev. Roum. Math. Pures Appl. 22 (1977), 295-297.
   MathSciNet

3. S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-449.
   MathSciNet     CrossRef

4. K. A. Challab, M. Darus and F. Ghanim, Inclusion relationships properties for certain subclasses of meromorphic functions associated with Hurwitz-Lerch zeta function, Italian Journal of Pure and Applied Mathematics 39 (2018), 410-423.

5. N. E. Cho, Y. S. Woo and S. Owa, Argument estimates of certain meromorphic functions, New extension of historical theorems for univalent function theory (Japanese) (Kyoto, 1999), Surikaisekikenkyusho Kokyuroku 1164 (2000), 1-11.
   MathSciNet

6. R. M. El-Ashwah, Inclusion properties regarding the meromorphic structure of Srivastava-Attiya operator, Southeast Asian Bull. Math. 38 (2014), 501-512.
   MathSciNet

7. R. M. El-Ashwah, Inclusion relationships properties for certain subclasses of meromorphic functions associated with Hurwitz-Lerch zeta function, Acta Univ. Apulensis 34 (2013), 191-205.
   MathSciNet

8. 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.
   MathSciNet     CrossRef

9. F. Ghanim, Certain properties of classes of meromorphic functions defined by a linear operator and associated with Hurwitz-Lerch zeta function, Advanced Studies in Contemporary Mathematics 27 (2017), 175-180.

10. F. Ghanim and M. Darus, Some properties on a certain class of meromorphic functions related to Cho-Kwon-Srivastava operator, Asian-Eur. J. Math. 5(4) (2012), Article ID 1250052, 1-9.
    MathSciNet     CrossRef

11. F. Ghanim and R. M. El-Ashwah, Inclusion properties of certain subclass of univalent meromorphic functions defined by a linear operator associated with Hurwitz–Lerch zeta function, Asian-Eur. J. Math. 10(4) (2017), 1-10.
    MathSciNet     CrossRef

12. A. Y. Lashin, On certain subclasses of meromorphic functions associated with certain integral operators, Comput. Math. Appl. 59 (2010), 524-531.
    MathSciNet     CrossRef

13. S. S. Miller and P. T. Mocanu, Differential Subordinations : Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker Incorporated, New York and Basel, 2000.
    MathSciNet

14. E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
    MathSciNet

15. H. M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000), 77-84.
    MathSciNet     CrossRef

16. H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz- Lerch zeta function and diferential subordination, Integral Transforms Spec. Funct. 18 (2007), 207-216.
    MathSciNet     CrossRef

17. H. M. Srivastava and J. Choi, Series Associated with Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
    MathSciNet     CrossRef

18. 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.
    MathSciNet     CrossRef

19. 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.
    MathSciNet     CrossRef

20. 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.
    MathSciNet     CrossRef

21. H. M. Srivastava, A. Y. Lashin and B. A. Frasin, Starlikeness and convexity of certain classes of meromorphically multivalent functions, Theory Appl. Math. Comput. Sci. 3 (2013), 93-102.

22. 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.
    MathSciNet

23. B. A. Uralegaddi and C. Somanatha, New criteria for meromorphic starlike univalent functions, Bull. Austral. Math. Soc. 43 (1991), 137-140.
    MathSciNet     CrossRef

24. 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, Fourth Edition, Cambridge University Press, Cambridge, London and New York, 1927.
    MathSciNet

25. D. R. Wilken and J. Feng, A remark on convex and starlike functions, J. London Math. Soc. (2) 21 (1980), 287-290.
    MathSciNet     CrossRef