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 Multivalent Meromorphic Functions with a Pole of Order p at the Origin

In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. We provide the conditions to obtain sufficient conditions for meromorphic starlikeness involving quasi-subordination. Our other main results include the solution to the Fekete–Szegő problem and inclusion relationships for functions belonging to the defined function classes. Several consequences of our main results are pointed out

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

Inclusion Properties for Certain Subclasses of Uniformly P-Valent Analytic Functions Involving Linear Operator

In this paper, the authors study some inclusion results for new subclasses of b-uniformly -valent functions in the open unit disc defined by differ-integral operator and some results of certain integral operator are also obtained

New Criteria for Meromorphic Multivalent Alpha-Convex Functions

The aim of the present paper is to obtain sufficient condition for the class of meromorphic p-valent alpha convex functions of order ξ and then to study mapping properties of the newly defined integral operators. Many known results appeared as special consequences of our work

CERTAIN SUBCLASSES OF P-VALENT MEROMORPHIC CONVEX FUNCTIONS ASSOCIATED WITH MOSTAFA OPERATOR

In this paper we study certain subclasses of analytic p-valent meromorphic convex functions with positive coefficients in the puncture unit disk. The result presented coefficient estimate, growth and distortion properties for functions belonging to this subclasses. Further results of modified hadamard product, inclusion properties, radii of close-to-convexity; starlikeness and convexity for functions belonging to the subclasses are discussed. Keywords: p-Valent meromorphic functions, convex function, Modified Hadamard product, inclusion properties and radii of starlikeness. AMS Subject Classification: 30C4