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In the present paper the new multiplier transformations$\mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l)$ $(\delta ,l\geq0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )}$ of multivalentfunctions is defined. Making use of the operator $\mathrm{%{\mathcal{J}}}_{p}^{\delta }(\lambda ,\mu ,l),$ two new subclasses $\mathcal{%P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}%_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$\textbf{\ }of multivalent analyticfunctions are introduced and investigated in the open unit disk. Someinteresting relations and characteristics such as inclusion relationships,neighborhoods, partial sums, some applications of fractional calculus andquasi-convolution properties of functions belonging to each of these subclasses$\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and$\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ areinvestigated. Relevant connections of the definitions and results presented inthis paper with those obtained in several earlier works on the subject are alsopointed out.

Certain subclasses of multivalent functions defined by new multiplier transformations