Properties of some families of meromorphic multivalent functions associated with generalized hypergeometric functions

Abstract

We introduce and study two subclasses ${\mathrm{\Omega }}_{[{\alpha }_1]}(A,B,\lambda )$ and ${\mathrm{\Omega }}_{[{\alpha }_1]}^{+}(A,B,\lambda )$of meromorphic $p$-valent functions defined by certain linear operator involving the generalized hypergeometric function. The main objectis to investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend thefamiliar concept of neighborhoods of analytic functions to these subclasses. We also derive many interesting results for the Hadamard products offunctions belonging to the class ${\mathrm{\Omega }}_{[{\alpha }_1]}^{+}(\alpha ,\beta ,\gamma ,\lambda )$.