Certain subclasses of multivalent functions defined by new multiplier transformations

In the present paper the new multiplier transformations \mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq 0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent functions 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 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 $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ 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

Subclasses of meromorphically multivalent functions defined by a differential operator

In this paper we introduce and study two new subclasses \Sigma_{\lambda\mu mp}(\alpha,\beta)$and$\Sigma^{+}_{\lambda\mu mp}(\alpha,\beta)$of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of$% (n,\delta)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions

Some Properties of Certain subclass of Meromorphically Multivalent Functions Defined by Convolution and Integral Operator involving I-Function

In the present paper, we introduce a certain subclass of meromorphic functions . We obtain some results, like, Coefficient inequality, Modified Hadamard Product, Integral means and Inclusion properties for this class

Certain classes of multivalent functions with negative coefficients associated with a convolution structure

Making use of a convolution structure, we introduce a new class of analytic functions $mathbb{T}^{p}_{g}(lambda,alpha, beta, )$ defined in the open unit disc and investigate its various characteristics. Further we obtained distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for functions belonging to the class $mathbb{T}^{p}_{g}(lambda,alpha, beta).

Some Geometric Properties Of Multivalent Convex Function For Operator On Hilbert Space

بالاستفادة من استعمال المؤثر على فضاء هلبرت، نحنُ  قدمنا ودرسنا بعض الخصائص الهندسية من الدوال التحليلية المتعددة التكافؤ المحدبة ذات معاملات سالبة.  للصنف الجزئي كذلك حصلنا على بعض الخصائص الهندسية، مثل، متراجحة المعاملات، مبرهنة النمو والتشوية، النقاط الحرجة، المجموعة المحدبة، نظرية الانغلاق، أنصاف الاقطار المغلقة، المتوسط الوزني وخواص الاحتواء لهذا الصنف.              By making use of the operator on Hilbert space, we introduce and study some properties of geometric of a subclass of multivalent convex functions with negative coefficients. Also, we obtain some geometric properties, such as coefficient inequality, growth and distortion theorem, extreme points, convex set, closure theorem, radius of close-to-convexity, weighted mean and inclusive properties

Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions

In the present investigation, with the help of certain higher- order q-derivatives, some new subclasses of multivalent q-starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient condition and certain coefficient inequalities for our defined function classes. Some known consequences related to this subject are also highlighted. Finally, the well-demonstrated fact about the (p, q)-variations is also given in the concluding section