Opuscula Math. 31, no. 4 (2011), 651-668

Opuscula Mathematica

On some classes of meromorphic functions defined by subordination and superordination

Alina Totoi

Abstract. Let \(p\in \mathbb{N}^*\) and \(\beta,\gamma\in \mathbb{C}\) with \(\beta\neq 0\) and let \(\Sigma_p\) denote the class of meromorphic functions of the form \(g(z)=\frac{a_{-p}}{z^p}+a_0+a_1 z+\ldots,\,z\in \dot U\), \(a_{-p}\neq 0\). We consider the integral operator \(J_{p,\beta,\gamma}:K_{p,\beta,\gamma}\subset\Sigma_p\to \Sigma_p\) defined by \[J_{p,\beta,\gamma}(g)(z)=\left[\frac{\gamma-p\beta}{z^\gamma }\int_0^zg^{\beta}(t) t^{\gamma-1}dt\right]^{\frac{1}{\beta}},\,g\in K_{p,\beta,\gamma},\,z\in \dot U.\] We introduce some new subclasses of the class \(\Sigma_p\), associated with subordination and superordination, such that, in some particular cases, these new subclasses are the well-known classes of meromorphic starlike functions and we study the properties of these subclasses with respect to the operator \(J_{p,\beta,\gamma}\).

Keywords: meromorphic functions, integral operators, subordination, superordination.

Mathematics Subject Classification: 30C45.

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  • Alina Totoi
  • “Lucian Blaga” University of Sibiu, Faculty of Science, Department of Mathematics, Str. Dr. I. Ratiu, no. 5, Sibiu, Romania
  • Received: 2010-07-07.
  • Revised: 2010-11-12.
  • Accepted: 2010-11-15.
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Cite this article as:
Alina Totoi, On some classes of meromorphic functions defined by subordination and superordination, Opuscula Math. 31, no. 4 (2011), 651-668, http://dx.doi.org/10.7494/OpMath.2011.31.4.651

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