Conditions for the univalence of certain integral operatos

Authors

  • Rasoul Aghalary
  • Ali Ebadian
  • Parviz Arjomandinia

DOI:

https://doi.org/10.5556/j.tkjm.44.2013.1199

Keywords:

integral operators, univalent functions.

Abstract

In the present paper, we consider two integral operators defined on special subclass of $\mathcal{A}$,namely $U_n(\lambda,\mu)$ with $n\in\mathbb{N}$. Using the extension of Becker's lemma, we obtain new univalence criterions for the operators in the open unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}.$ Finally, we deduce some corollaries of the main results.

Author Biographies

Rasoul Aghalary

Department ofMathematics, Faculty of Science, Urmia University, Urmia, Iran.

Ali Ebadian

Department ofMathematics, Faculty of Science, Urmia University, Urmia, Iran.

Parviz Arjomandinia

Department ofMathematics, Faculty of Science, Urmia University, Urmia, Iran.

References

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N. Pascu, An improvement of Becker's univalence criterion (Proceedings of the Commemorative Session Simion Stoilow, Brasov, (1987), 43--48.

V. Pescar, A new generalization of Ahlfor's and Becker's criterion of univalence, Bull. Malays. Math. Soc., 19,(1996), 53--54.

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S. Ponnusamy and P. Sahoo, Geometric properties of certain linear integral transforms, Bull. Belg. Math. Soc. Simon Stevin, 12,(2005), 95--108.

N. Seenivasagan, Sufficient conditions for univalence, Appl. Math. E-notes, 8(2008), 30--35.

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Published

2012-12-10

How to Cite

Aghalary, R., Ebadian, A., & Arjomandinia, P. (2012). Conditions for the univalence of certain integral operatos. Tamkang Journal of Mathematics, 44(4), 387–393. https://doi.org/10.5556/j.tkjm.44.2013.1199

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Section

Papers