Title: Families of Meromorphic Multivalent Functions Associated with the Dziok-Raina Operator
Author(s): G. Murugusundaramoorthy, M.K. Aouf
Pages: 1-18
Cite as:
G. Murugusundaramoorthy, M.K. Aouf, Families of Meromorphic Multivalent Functions Associated with the Dziok-Raina Operator, Int. J. Anal. Appl., 2 (1) (2013), 1-18.

Abstract


Making use a linear operator, which is defined here by means of the Hadamard product (or convolution), involving the Wright’s generalized hypergeometric function , we introduce two novel subclassesP p(q,s,α1;A,B,λ) andP+p(q,s,α1;A,B,λ) of meromorphically multivalent functions oforder λ(0 ≤ λ < p) in the punctured disc U∗. In this paper we investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions . We also derive many interesting results for the Hadamard products of functions belonging to the classP+p(q,s,α1;A,B,λ).

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References


  1. O. Altintas and S. Owa, Neighborhoods of certain analytic functions with negative coefficients, Internat. J. Math. Math. Sci. 19(1996), 797-800.

  2. O. Altintas, O. Ozkan and H. M. Srivastava, Neighborhoods of a class of analytic functions with negative coefficients, Appl. Math. Lett. 13(2000), no. 3, 63-67.

  3. O. Altintas, O. Ozkan and H. M. Srivastava, Neighborhoods of a certain family of multivalent functions with negative coefficients, Comput. Math. Appl. 47(2004), 1667-1672.

  4. M. K. Aouf, On a class of meromorphic multivalent functions with positive coefficients, Math. Japon. 35(1990), 603-608.

  5. M. K. Aouf, A generalization of meromorphic multivalent functions with positive coefficients, Math. Japon. 35(1990), 609-614.

  6. M. K. Aouf and H. M. Hossen, New criteria for meromorphic p-valent starlike functions, Tsukuba J. Math. 17(1993), 481-486.

  7. M. K. Aouf, H. M. Hossen and H. E. Elattar, A certain class of meromorphic multivalent functions with positive and fixed second coefficients, Punjab Univ. J. Math. 33(2000), 115-124.

  8. J. Dziok and R. K. Raina, Families of analytic functions associated with the Wright generalized hypergemetrric function , Demonstratio Math. 37 (2004), no.3, 533-542.

  9. J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103(1999), 1-13.

  10. J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct. 14(2003), 7-18.

  11. A. Gangadharan, T. N. Shanmugam and H. M. Srivastava, Generalized hypergeometric functions associated with k-uniformly convex functions, Comput. Math. Appl. 44(2002), no. 12, 1515-1526.

  12. A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8(1957), 598-601.

  13. I. S. Jack, Functions starlike and convex functions of order α, J. London Math. Soc. (Ser. 2) 2(1971), no. 3, 469-474.

  14. S. B. Joshi and M. K. Aouf, Meromorphic multivalent functions with positive and fixed second coefficients, Kyungpook Math. J. 35(1995), 163-169.

  15. S. B. Joshi and H. M. Srivastava, A certain family of meromorphically multivalent functions, Comput. Math. Appl. 38(1999), no. 3-4, 201-211.

  16. S. R. Kulkarni, U. H. Naik and H. M. Srivastava, A certain class of meromorphically p-valent quasi-convex functions, PanAmer. Math. J. 8(1998), no. 1, 57-64.

  17. J. -L. Liu, Properties of some families of meromorphic p-valent functions, Math. Japon. 52(2000), no. 3, 425-434.

  18. J. -L. Liu, Strongly starlike functions associated with the Dziok-Srivastava operator, Tamkang J. Math. 35(2004), no. 1, 37-42.

  19. 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.

  20. J. -L. Liu and H. M. Srivastava, Subclasses of meromorphically multivalent functions associated with a certain linear operator, Math. Comput. Modelling 39(2004), 35-44.

  21. J. -L. Liu and H. M. Srivastava, Classes of meromorphically multivalent functions associated with the generalized hypergeometric function, Math. Comput. Modelling 39(2004), 21-34.

  22. M. L. Mogra, Meromorphic multivalent functions with positive coefficients. I, Math. Japon. 35(1990), no. 1, 1-11.

  23. M. L. Morga, Meromorphic multivalent functions with positive coefficients. II, Math. Japon. 35(1990), no. 6, 1089-1098.

  24. S. Owa, H. E. Darwish and M. K. Aouf, Meromorphic multivalent functions with positive and fixed second coefficients, Math. Japon. 46(1997), no. 2, 231-236.

  25. R. K. Raina, On certain classes of analytic functions and applications to fractional calculus operators , Integral Tranform. Spec. Funct. 5(1997), 247-260..

  26. R. K. Raina and T. S. Nahar, A note on boundedness properties of Wright’s generalized hypergeometric function, Ann. Math. Blaise Pascal 4 (1997), 83-95.

  27. R. K. Raina and T. S. Nahar, On characterization of certain Wright’s generalized hypergeometric functions involving certain subclasses of analytic functions, Informatica 10 (1999), 219-230.

  28. R. K. Raina and T. S. Nahar, On univalent and starlike Wright’s hypergeometric functions, Rend. Sem. Math. Univ. Padava 95 (1996) , 11-22.

  29. R. K. Raina and H. M. Srivastava, A new class of meromorphically multivalent functions with applications to generalized hypergeometric functions, Math. Comput. Modelling 43(2006), 350-356.

  30. St. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81(1981), 521-527.

  31. A. Schild and H. Silverman, Convolution of univalent functions with negative coefficients, Ann. Univ. Mariae CurieSklodowska Sect. A, 29(1975), 99-107.

  32. H. M. Srivastava H. M. Hossen and M. K. Aouf, A unified presentation of some classes of meromorphically multivalent functions, Comput. Math. Appl. 38(1999), 63-70.

  33. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press ( Ellis Horwood Ltd., Chichester ), John Wiley and Sons, New York , Chichester, Brisbane and London 1985.

  34. B. A. Uralegaddi and C. Somanatha, Certain classes of meromorphic multivalent functions, Tamkang J. Math. 23(1992), 223-231.

  35. B. A. Uralegaddi and C. Somanatha, Certain classes of meromorphic multivalent functions , Tamkang J. Math. 23 (1992), 223-231.

  36. E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc. 46 (1946), 389-408.

  37. D. -G. Yang, On new subclasses of meromorphic p-valent functions, J. Math. Res. Exposition 15(1995), 7-13.

  38. D. -G. Yang, Subclasses of meromorphic p-valent convex functions, J. Math. Res. Exposition 20(2000), 215-219.