Integral Operator Defined by k-th Hadamard Product

Authors

  • Maslina Darus School of Mathematical Sciences Faculty of science and Technology, Universiti Kebangsaan Malaysia Bangi 43600, Selangor Darul Ehsan, Malaysia
  • Rabha W. Ibrahim School of Mathematical Sciences Faculty of science and Technology, Universiti Kebangsaan Malaysia Bangi 43600, Selangor Darul Ehsan, Malaysia

DOI:

https://doi.org/10.5614/itbj.sci.2010.42.2.5

Abstract

We introduce an integral operator on the class A of analytic functions in the unit disk involving k { th Hadamard product (convolution) corresponding to the differential operator defined recently by Al-Shaqsi and Darus. New classes containing this operator are studied. Characterization and other properties of these classes are studied. Moreover, subordination and superordination results involving this operator are obtained.

References

Al-Shaqsi, K. & Darus, M., Differential subordination with generalized derivative operator. (to appear in AJMMS)

Darus, M. & Ibrahim, R., Generalization of differential operator, Journal of Mathematics and Statistics 4(3), pp. 138-144, 2008.

Salagean, G.S., Subclasses of univalent functions, Lecture Notes in Math., 1013, Springer-Verlag, Berlin, pp. 362-372, 1983.

Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math. Soc., 49, 109-115, 1975.

Al-Oboudi, F.M., On univalent functions defined by a generalized Salagean operator, I.J.M.M.S, 27, pp. 1429-1436, 2004.

Al-Shaqsi, Darus, M., An operator defined by convolusion involving polylogarthms functions, Journal of Mathematics and Statistics, 4(1), pp. 46-50, 2008.

Noor, K.I., On new classes of integral operators, J.Nat.Geomet. 16, pp. 71-80, 1999.

Noor, K.I. & Noor, M.A., On integral operators, J. of Math. Analy. and Appl. 238, pp. 341-352, 1999.

Brickman, L., { like analytic functions, I.Bull. Amer. Math. Soc. 79, pp. 555-558, 1973.

Bulboaca, T., Classes of first-order differential superordinations, Demonstr.Math. 35(2), pp. 287-292, 2002.

Miller, S.S. & Mocanu, P.T., Subordinants of differential superordinations, Complex Variables, 48(10), pp.815-826, 2003.

Miller, S.S. & Mocanu, P.T., Differential Subordinantions: Theory and Applications. Pure and Applied Mathematics, 225, Dekker, New York, 2000.

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