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).

Full Text: PDF

 

References


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

  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. Google Scholar

  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. Google Scholar

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

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

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

  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. Google Scholar

  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. Google Scholar

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

  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. Google Scholar

  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. Google Scholar

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

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

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

  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. Google Scholar

  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. Google Scholar

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

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

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

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

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

  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. Google Scholar

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

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

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

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

  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. Google Scholar

  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. Google Scholar

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

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

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

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

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