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

Strong Subordination for E -valent Functions Involving the Operator Generalized Srivastava-Attiya

          الموضوع المقدم في هذا البحث  يتضمن التحري عن  بعض العلاقات  وبعض الخواص المهمة  للدوال متعددة التكافوء التي تتعامل مع موثر(( Srivastava-Attiyaالمعمم بواسطة استخدام  مبادئ  التبعية التفاضلية القوية.Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination

On some first-order differential subordination

AbstractLet A denote the class of functions f that are analytic in the unit disc D and normalized by f(0)=f′(0)−1=0. In this paper, we investigate the class of functions such that Re{f′(z)+zf″(z)-β}>α in D. We determine conditions for α and β under which the function f is univalent, close-to-convex, and convex. To obtain this, we first estimate ∣Arg{f′(z)}∣ which improves the earlier results

Majorization for a Class of Analytic Functions Defined by q

We introduce a new class of multivalent analytic functions defined by using q-differentiation and fractional q-calculus operators. Further, we investigate majorization properties for functions belonging to this class. Also, we point out some new and known consequences of our main result

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