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A linear operator and associated class of multivalent analytic functions

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Języki publikacji
EN
Abstrakty
EN
We introduce a certain class H alpha/k (p, lambda;h) of multivalent analytic functions in the open unit disc involving a linear operator L alpha/k. The aim of this paper is to extend the similar concept of many earlier papers. We use techniques of differential subordination and convolution of this class.
Wydawca
Rocznik
Strony
559--566
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
  • Department of Mathematics Rzeszów University of Technology ul. W. Pola 2, 35-959 Rzeszów, Poland, jsokol@prz.edu.pl
Bibliografia
  • [1] B. C. Carlson, D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745.
  • [2] N. E. Cho, O.S. Kwon, Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations, J. Math. Anal. Appl. 300 (2004), 505-520.
  • [3] J. Dziok, H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct. 14 (2003), 7-18.
  • [4] J. Dziok, H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13.
  • [5] S. Fukui, J. A. Kim, H. M. Srivastava, On certain subclasses of univalent functions by some integral operators, Math. Japonica, 50 (1999), 359-370.
  • [6] D. I. Hallenbeck, St. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc. 52 (1975), 191-195.
  • [7] J.-L. Liu, H. M. Srivastava, A linear operator and associated families of meromor-phically multivalent functions, J. Math. Anal. Appl. 259 (2001), 566-581.
  • [8] J.-L. Liu, H. M. Srivastava, Classes of meromorphically multivalent Functions associated with the generalized hypergeometric function, Math, and Comp. Modelling 39 (2004), 21-34.
  • [9] J.-L. Liu, H. M. Srivastava, Certain properties of the Dziok-Srivastava operator, Appl. Math. Comput. 159 (2004), 485-493.
  • [10] S. S. Miller, P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157-171.
  • [11] K. I. Noor, Some classes of p-valent analytic functions defined by certain integral operator, Appl. Math. Comput. 157 (2004), 835-840.
  • [12] M. L. Morga, On a class of univalent functions whose derivatives have a positive real part, Riv. Math. Univ. Parma 7 (1981), 163-172.
  • [13] J. Patel, P. Sahoo, Properties of a Class of Multivalent Analytic Functions, Comp. Math. Appl. 46 (2003), 1633-1644.
  • [14] St. Ruscheweyh, J. Stankiewicz, Subordination under convex univalent functions, Bull. Polon. Acad. Sci., Math. 33 (1985), 499-502.
  • [15] H. Saitoh, A linear operator and its applications of first order differential subordinations, Mat. Japonica 44 (1996), 31-38.
  • [16] H. Saitoh, M. Nunokawa, On certain subclasses of analytic functions involving a linear operator, Surikaisekikenkyusho Kokyuroku 936 (1996), 97-109.
  • [17] R. Singh, S. Singh, Convolution properties of a class of starlike functions, Proc. Amer. Math. Soc. 108 (1989), 145-152.
  • [18] N. S. Sohi, A class of p-valent analytic functions, Indian J. Pure Appl. Math. 10(7) (1979), 826-834.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0035-0005
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