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ON CERTAIN CLASSES OF MULTIVALENT FUNCTIONS INVOLVING A GENERALIZED DIFFERENTIAL OPERATOR

  • Selvaraj, Chellian (DEPARTMENT OF MATHEMATICS PRESIDENCY COLLEGE(AUTONOMOUS)) ;
  • Selvakumaran, Kuppathai A. (DEPARTMENT OF MATHEMATICS R.M.K. ENGG. COLLEGE)
  • Published : 2009.09.30

Abstract

Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.

Keywords

References

  1. S. S. Miller and P. T. Mocanu, On some classes of first-order differential subordinations, Michigan Math. J. 32 (1985), no. 2, 185–195 https://doi.org/10.1307/mmj/1029003185
  2. S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Differential Equations 67 (1987), no. 2, 199–211 https://doi.org/10.1016/0022-0396(87)90146-X
  3. S. Owa, Z. Wu, and F. Y. Ren, A note on certain subclass of Sakaguchi functions, Bull. Soc. Roy. Sci. Liege 57 (1988), no. 3, 143–149
  4. F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), no. 1, 189–196
  5. K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72–75
  6. C. Selvaraj and C. Santhosh Moni, Classes of analytic functions of complex order involving a family of generalised linear operators, Pre-print
  7. N.-E. Xu and D.-G. Yang, Some classes of analytic and multivalent functions involving a liner operator, Mathematical and Computer Modelling (2008), doi: 10.1016/ j.mcm.2008.04.005 - In press
  8. N.-E. Xu and D.-G. Yang, An application of differential subordinations and some criteria for starlikeness, Indian J. Pure Appl. Math. 36 (2005), no. 10, 541–556
  9. D.-G. Yang and J.-L. Liu, On Sakaguchi functions, Int. J. Math. Math. Sci. 2003, no. 30, 1923–1931 https://doi.org/10.1155/S0161171203205330
  10. Z.-G. Wang, Y.-P. Jiang, and H. M. Srivastava, Some subclasses of multivalent analytic functions involving the Dziok-Srivastava operator, Integral Transforms Spec. Funct. 19 (2008), no. 1-2, 129–146 https://doi.org/10.1080/10652460701635456

Cited by

  1. Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator vol.22, pp.1, 2014, https://doi.org/10.1016/j.joems.2013.06.009
  2. On sandwich theorems for multivalent functions involving a generalized differential operator vol.61, pp.9, 2011, https://doi.org/10.1016/j.camwa.2011.02.050