Univalence criteria for a nonlinear integral operator

Authors

  • C. Selvaraj Department of Mathematics, Presidency College (Autonomous), Chennai-600 005, India.
  • K. A. Selvakumaran Department of Mathematics, R.M.K. Engg. College, Kavaraipettai-601 206, India.

DOI:

https://doi.org/10.5556/j.tkjm.42.2011.867

Keywords:

Univalent functions, subordination, Dziok-Srivastava operator, integral transform. 79

Abstract

The purpose of this paper is to obtain univalence of a certain nonlinear integral transform of functions belonging to a subclass of analytic functions. We also give several interesting geometric properties of the integral transform.

References

R. Aghalary, S. B. Joshi, R. N. Mohapatra, V. Ravichandran, Subordinations for analytic functions defined by the Dziok-Srivastava linear operator, Appl.Math. Comput., 187 (2007), 13–19.

J. Becker, Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen, J. Reine Angew.Math., 255 (1972), 23–43.

D. Breaz and N. Breaz, Two integral operators, Studia Univ. Babe¸s BolyaiMath. 47 (2002), 13–19.

D. Breaz, N. Breaz and H.M. Srivastava, An extension of the univalent condition for a family of integral operators, Appl.Math. Lett., 22 (2009), 41–44.

J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl.Math. Comput. 103 (1999), 1–13.

J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14 (2003), 7–18.

Y. C. Kim, S. Ponnusamy and T. Sugawa, Geometric properties of nonlinear integral transforms of certain analytic functions, Proc. Japan Acad. Ser. AMath. Sci., 80 (2004), 57–60.

Y. C. Kim and H. M. Srivastava, Geometric properties of certain non-linear integral operators, Integral Transforms Spec. Funct., 17 (2006), 723–732.

Y. J. Kim and E. P. Merkes, On an integral of powers of a spirallike function, Kyungpook Math. J., 12 (1972), 249–252.

J.-L. Liu and H.M. Srivastava, A class ofmultivalently analytic functions associated with the Dziok-Srivastava operator, Integral Transforms Spec. Funct., 20 (2009), 401–417.

G. I. Oros, G. Oros and D. Breaz, Sufficient conditions for univalence of an integral operator, J. Inequal. Appl., 2008, Art. ID 127645, 7 pp.

V. Singh and P. N. Chichra, An extension of Becker’s criterion of univalence, J. Indian Math. Soc. (N.S.) 41(1977), 353–361, (1978).

H.M. Srivastava, D.-G. Yang and N.-E. Xu, Subordinations formultivalent analytic functions associated with the Dziok-Srivastava operator, Integral Transforms Spec. Funct., 20 (2009), 581–606.

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), 129–146.

Downloads

Published

2011-03-01

How to Cite

Selvaraj, C., & Selvakumaran, K. A. (2011). Univalence criteria for a nonlinear integral operator. Tamkang Journal of Mathematics, 42(1), 79–85. https://doi.org/10.5556/j.tkjm.42.2011.867

Issue

Section

Papers