由新的乘子变换定义的多叶函数的某些子类
Certain subclasses of multivalent functions defined by new multiplier transformations
摘要：
本文定义了多叶函数的新乘子变换$\mathrm{{\mathcal{J}% }}_{p}^{δ}(λ,μ,l)$ $(δ,l\geq 0,\;λ\geq μ\geq 0;\;p\in \mathrm{% }%\mathbb{N} )}$。利用算子$\mathrm{% {\mathcal{J}}}_{p}^{δ}(λ,μ,l),$，在开单位圆盘上引入并研究了多叶解析函数的两个新子类$\mathcal{% P}_{λ,μ,l}^{δ}(A,B;σ,p)$和$\widetilde{\mathcal{P}}% _{λ,μ,l}^{δ}(A,B;σ,p)$ \textbf{\ }.研究了$\mathcal{P}_{λ,μ,l}^{δ}(A,B;σ,p)$和$\widetilde{\mathcal{P}}_{λ,μ,l}^{δ}(A,B;σ,p)$子类中函数的包含关系、邻域、部分和、分数阶微积分的一些应用以及拟卷积性质等有趣的关系和特征.本文中提出的定义和结果与在几个早期的作品中获得的有关的连接也被指出。
英文摘要：
In the present paper the new multiplier transformations $\mathrm{{\mathcal{J}% }}_{p}^{δ}(λ,μ,l)$ $(δ,l\geq 0,\;λ\geq μ\geq 0;\;p\in \mathrm{% }%\mathbb{N} )}$ of multivalent functions is defined. Making use of the operator $\mathrm{% {\mathcal{J}}}_{p}^{δ}(λ,μ,l),$ two new subclasses $\mathcal{% P}_{λ,μ,l}^{δ}(A,B;σ,p)$ and $\widetilde{\mathcal{P}}% _{λ,μ,l}^{δ}(A,B;σ,p)$\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $\mathcal{P}_{λ,μ,l}^{δ}(A,B;σ,p)$ and $\widetilde{\mathcal{P}}_{λ,μ,l}^{δ}(A,B;σ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
