TY  - JOUR
ID  - Totoi2011
LB  - Totoi2011
AU  - Totoi, Alina
TI  - On some classes of meromorphic functions defined by subordination and superordination
ST  - On some classes of meromorphic functions defined by subordination and superordination
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2011
VL  - 31
IS  - 4
SP  - 651
EP  - 668
DO  - http://dx.doi.org/10.7494/OpMath.2011.31.4.651
UR  - http://dx.doi.org/10.7494/OpMath.2011.31.4.651
AB  - 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 \(J_{p,\beta,\gamma}\).
KW  - meromorphic functions
KW  - integral operators
KW  - subordination
KW  - superordination
SN  - 1232-9274
ER  -