A Class of Multivalent Analytic Functions Defined by a New Linear Operator

Volume 8, Issue 4, pp 326-334 http://dx.doi.org/10.22436/jmcs.08.04.01

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2610 Downloads
• 4227 Views

Authors

Rahim Kargar - Department of Mathematics, Payame Noor University, I. R. of IRAN. Abdoljalil Bilavi - Department of Mathematics, Shoush Branch, Islamic Azad University, Shoush, Iran. Salahaddin Abdolahi - Department of Mathematics, Payame Noor University, I. R. of IRAN. Salah Maroufi - Department of Mathematics, Payame Noor University, I. R. of IRAN.

Abstract

The main object of the present paper is to derive some results for multivalent analytic functions defined by a linear operator. Making use of a certain operator, which is defined here by means of Hadamard product, we introduce a subclasses \(S_{A,B}^{p,\gamma}(\alpha,\lambda,\mu,\nu,a,c)\) of the class \(A(p)\) of normalized p-valent analytic functions on the open unit disk. Also we have extended some of the previous results and have given necessary and sufficient condition for this class.

Share and Cite

Keywords

• Analytic functions
• Multivalent functions
• Hadamard product
• Subordination
• Linear operators.

MSC

•  30C45
•  30C50

References

• [1] M. K. Aouf , A generalization of multivalent functions defined by Ruscheweyh derivatives, Soochow J. Math. , 17 (1991), 83-97.
  • MathSciNet
  • Google Scholar


• [2] M. K. Aouf, On certain subclass of analytic 𝑝-valent function, II, Math. Japan., 34 (1989), 683-691.
  • MathSciNet
  • Google Scholar


• [3] B. C. Carlson, D. B. Shaffer, Starlike and prstarlike hypergeometric functions, SIAM J. Math. Anal. , 15 (1984), 737-745.
  • View Article
  • Google Scholar


• [4] M. P. Chen, A class of 𝑝-valent functions, Soochow J. Math. , 8 (1982), 15-26.


• [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.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] Jae Ho Choi, On differential subordinations of multivalent functions involving a certain fractional derivative operator, International Journal of Mathematics and Mathematical Sciences, (2010), 1-10.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] J. H. Choi, M. Saigo, H. M. Srivastava, Some inclusion properties of a certain family of integral opertaors, J. Math. Anal. Appl. , 276 (2002), 432-445.
  • View Article
  • Google Scholar


• [8] J. Dziok, Classes of analytic funcions involving some integral operator, FoliaSci. Univ. Tech. Resoviensis , 20 (1995), 21-39.
  • Google Scholar


• [9] R. M. Goel, N. S. Sohi, A new criterion for \(p\)-valent functions, Proc. Amer. Math. Soc. , 78 (1980), 353-357.
  • View Article
  • MathSciNet
  • Google Scholar


• [10] R. M. Goel, N. S. Sohi , New criteria for \(p\)-valence, Indian J. Pure Appl. Math. , 11 (1980), 1356-1360.
  • MathSciNet
  • Google Scholar
  • MATH


• [11] Yu. E. Hohlov, Operators and operations in the class of univalent functions, Izv, Vvssh. Ucebn. Zaved. Math. (in Russian)., 10 (1987), 83-89
  • Google Scholar


• [12] V. Kumar, S. L. Shukla, Multivalent function defined by Ruscheweyh derivatives, II, Indian J. Pure Appl. Math. , 15 (1984), 1228-1238.
  • Google Scholar


• [13] J. L. Liu, K. I. Noor , Some properties of Noor integral operator, J. Natur. Geom., 21 (2002), 81-90.
  • MathSciNet
  • Google Scholar


• [14] B. S. Mehrok , A class of univalent functions, Tamkang J. Math , 13 (1982), 141-155.
  • Google Scholar


• [15] S. Owa , On certain subclass of analytic 𝑝-valent function , Math. Japon. , 29 (1984), 191-198.
  • MathSciNet
  • Google Scholar


• [16] S. Owa, On the distortion theorems, I. Kyungpook Math. J. , 18 (1978), 53-59.


• [17] S. Owa, H. M. Srivastava, Univalent starlike generalized hypergeometric functions, Canad. J. Math. , 39 (1987), 1057-1077.
  • View Article
  • MathSciNet
  • Google Scholar


• [18] S. Rusheweyh, New criteria for univalent functions , Proc. Amer. Math. Soc. , 49 (1975), 109-115.
  • View Article
  • Google Scholar


• [19] H. Saitoh, A liner operator and its applications of first order deffrential subodinations, Math. Japon. , 44 (1996), 31-38.
  • Google Scholar


• [20] H. M. Srivastava, M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients, I. J. of Mathematical Analysis and Applications, 171 (1992), 1-13.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH