Published July 22, 2010 | Version 8032

Certain Conditions for Strongly Starlike and Strongly Convex Functions

Description

In the present paper, we investigate a differential subordination involving multiplier transformation related to a sector in the open unit disk E = {z : |z| < 1}. As special cases to our main result, certain sufficient conditions for strongly starlike and strongly convex functions are obtained.

Files

8032.pdf

Files (212.1 kB)

Name Size Download all
md5:b75b3711fc3dbeca25499f9804c28edb
212.1 kB Preview Download

Additional details

References

  • R. Aghalary, R. M. Ali, S. B. Joshi and V. Ravichandran, Inequalities for analytic functions defined by certain linear operators, Int. J. Math. Sci., 4(2005), 267-274.
  • N. E. Cho and T. H. Kim, Multiplier transformations and strongly closeto- convex functions, Bull. Korean Math. Soc., 40(2003), 399-410.
  • N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, 37(2003), 39-49.
  • Jian Li and S. Owa, Properties of the S╦ÿal╦ÿagean operator, Georgian Math. J., 5(4)(1998), 361-366.
  • S. S. Miller and P. T. Mocanu, Marx-Strohh┬¿acker differential subordination systems, Proc. Amer. Math. Soc., 99(1987), 527-534.
  • Gh. Oros, A Condition for Starlikeness, General Mathematics, 7(1999), 1-6.
  • S. Owa, C. Y. Shen and M. Obradovi'c, Certain subclasses of analytic functions, Tamkang J. Math., 20(1989), 105-115.
  • G. S. S╦ÿal╦ÿagean, Subclasses of univalent functions, Lecture Notes in Math., 1013, 362-372, Springer-Verlag, Heideberg, 1983.
  • B. A. Uralegaddi, Certain subclasses of analytic functions, New Trends In Geometric Functions Theory and Applications. (Madras, 1990) 159-161, World Scientific Publishing Company, Singapore, New Jersey, Londan and Hong Kong, 1991.