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Certain class of p-valent functions associated with the wright generalized hypergeometric function

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EN
Abstrakty
EN
Using the Wright's generalized hypergeometric function, we introduce a new class Wk (p, q, s; A, B, lambda) of analytic p-valent functions with negative coefficients. In this paper we investigate coefficients estimates, distortion theorem, the radii of p-valent starlikeness and p-valent convexity and modified Hadamard products.
Wydawca
Rocznik
Strony
39--54
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
autor
autor
autor
  • Department of Mathematics Faculty of Science Mansoura University Mansoura 35516, Egypt, mkaouf127@yahoo.com
Bibliografia
  • [1] M. K. Aouf, Certain class of analytic functions associated with the generalized hyper-geometric function, J. Math. Appl. 29 (2007), 13-17
  • [2] M. K. Aouf, J. Dziok, Certain class of analytic functions associated with the Wright generalized hypergeometric function, J. Math. Appl. 30 (2008), 23-32.
  • [3] M. K. Aouf, H. Silverman, H. M. Srivastava, Some subclasses of functions involving a certain linear operator, Adv. Stud. Contemp. Math. 14 (2007), 215-232.
  • [4] S. D. Bernardi, Convex and univalent functions, Trans. Amer. Math. Soc. 135 (1996), 429-446.
  • [5] N. E. Cho, O. H. Kwon, H. M. Srivastava, Inclusion and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004), 470-483.
  • [6] J. Dziok, R. K. Raina, Families of analytic functions associated with the Wright generalized hypergeometric function, Demonstratio Math. 37 (2004), 533-542.
  • [7] J. Dziok, R. K. Raina, H. M. Srivastava, Some classes of analytic functions associated with operators on Hilbert space involving Wright hyper geometric function, Proc. Jangieon Math. Soc. 7 (2004), 43-55.
  • [8] J. Dziok, H. M. Srivastava, Classes of analytic functions with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13.
  • [9] J. Dziok, H. M. Srivastava, Certain subclasses of analytic functions associated with the Wright generalized hypergeometric function, Integral Transform. Spec. Funct. 14 (2003), 7-18.
  • [10] A. Gangadharan, T. N. Shanmugam, H. M. Srivastava, Generalized hypergeometric function associated with k-uniformly convex functions, Comput. Math. Appl. 44 (2002), 1515-1526.
  • [11] P. W. Karlsson, H. M. Srivastava, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Ltd, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and London, 1985.
  • [12] V. Kumar, S. L. Shukla, Multivalent functions defined by Ruscheweyh derivatives, Indian J. Pure Appl. Math. 15 (1984), 1216-1227.
  • [13] V. Kumar, S. L. Shukla, Multivalent functions defined by Ruscheweyh derivatives II, Indian J. Pure Appl. Math. 15 (1984), 1228-1238.
  • [14] R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1969), 755-758.
  • [15] J.-L. Liu, Strongly starlike functions associated with the Dziok-Srivastava operator, Tamkang J. Math. 35 (2004), 37-42.
  • [16] J.-L. Liu, K. I. Noor, Some properties of Noor integral operator, J. Natur. Geom. 21 (2002), 81-90.
  • [17] A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 17 (1966), 352-357.
  • [18] S. Owa, On the distortion theorems, I, Kyungpook Math. J. 18 (1978), 53-59.
  • [19] S. Owa, On certain classes of p-valent functions with negative coefficients, Simon Stevin 59 (1985), 385-402.
  • [20] S. Owa, H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057-1077.
  • [21] R. K. Raina, T. S. Nahar, A note on boundedness properties of Wright’s generalized hypergeometric function, Ann. Math. Blaise Pascal 4 (1997), 83-95.
  • [22] R. K. Raina, T. S. Nahar, On characterization of certain Wright’s generalized hyper-geometric functions involving certain subclasses of analytic functions, Informatica 10 (1999), 219-230
  • [23] R. K. Raina, T. S. Nahar, On univalent and starlike Wright’s hypergeometric functions, Rend. Sem. Math. Univ. Padova 95 (1996), 11-22.
  • [24] H. Saitoh, A linear operator and its applications of first order differential subordinations, Math. Japon. 44 (1996), 31-38.
  • [25] A. Schild, H. Silverman, Convolution univalent functions with negative coefficient, Ann. Univ. Mariae Curie-Skłodowska Sect. A 29 (1975), 99-107.
  • [26] H. M. Srivastava, M. K. Aouf, A certain fractional derivative operator and its application to a new class of analytic and multivalent functions with negative coefficients I and II, J. Math. Anal Appl. 171 (1992), 1-13; 192 (1995), 673-688.
  • [27] E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc. 46 (1946), 389-408
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0027-0025
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