Inclusion relationships for certain subclasses of meromorphic functions defined by using the extended multiplier transformations
Summary: Let \(\sum\) denote the class of analytic functions in the punctured unit disc \(U^{\ast} = \{z : 0 < |z| < 1\}\). Set \[ \varphi^m_{\lambda,\ell}(z) = 1/z + \sum^\infty_{k=0} [\ell + \lambda (k + 1)/\ell]^m z^k\quad (m \in \mathbb N_0; \ell > 0; \lambda \geq 0; z \in U^\ast), \] and define \(\varphi^{m,\mu}_{\lambda,\ell}\) in terms of the Hadamard product by \(\varphi^m_{\lambda,\ell} (z) \ast \varphi^{m,\mu}_{\lambda,\ell} (z) = 1/z(1 - z)^\mu\) (\(\mu > 0; z \in U^\ast\)). In this paper, we introduce several new subclasses of analytic functions defined by means of the operator \(I^m_\mu (\lambda, \ell)f(z) = \varphi^{m,\mu}_{\lambda,\ell} (z) \ast f(z)\) (\(f \in \sum; m \in \mathbb N_0; \ell > 0; \lambda \geq 0; \mu > 0\)). Inclusion properties of these classes and some applications involving integral operators are also considered.
scientific article; zbMATH DE number 5964883
scientific article