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On Applications of Differential Subordination to Certain Subclass of Multivalent Functions

Aghalary, Rasoul;Wang, Zhi-Gang

  • Received : 2008.03.11
  • Accepted : 2008.06.03
  • Published : 2009.06.30

Abstract

In the present paper, we introduce and investigate a new subclass of multivalent functions associated with the Cho-Kwon-Srivastava operator $\tau^{\lambda}_p(a,c)$. Such results as inclusion relationships, convolution properties and criteria for starlikeness are proved. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.

Keywords

Cho-Kwon-Srivastava operator;differential subordination;Hadamard product (or convolution);starlike and convex functions

References

  1. R. Aghalary, On subclasses of p-valent analytic functions defined by integral operators, Kyungpook Math. J., 47(2007), 393-401.
  2. N. E. Cho, O. S. Kwon and H. M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292(2004), 470-483. https://doi.org/10.1016/j.jmaa.2003.12.026
  3. D. J. Hallenbeck and St. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc., 52(1975), 191-195. https://doi.org/10.1090/S0002-9939-1975-0374403-3
  4. J. Patel, On certain subclasses of multivalent functions involving Cho-Kwon-Srivastava operator, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 60(2006), 75-86.
  5. St. Ruscheweyh and J. Stankiewicz, Subordination and convex univalent functions, Bull. Pol. Acad. Sci. Math., 33(1985), 499-502.
  6. S. Ruscheweyh, New ceriteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109-115. https://doi.org/10.1090/S0002-9939-1975-0367176-1
  7. J. Sokol and L. Trojnar-Spelina, Convolution properties for certain classes of multivalent functions, J. Math. Anal. Appl., 337(2008), 1190-1197. https://doi.org/10.1016/j.jmaa.2007.04.055