Certain Subclasses Of Multivalent Functions Research Articles

A Certain Subclass of Multivalent Functions Associated with Borel Distribution Series

In this paper, we determine the necessary and sufficient conditions for the power series f(z) whose coefficients are probabilities of the Borel distribution to be in the family J(p,λ ,α,β,γ) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral representation, radii of starlikeness and convexity. Also we discuss the extreme points and neighborhood property for functions belongs to this family.

On certain subclasses of multivalent functions with varying arguments of coefficients

In this paper we introduce and study new classes VM_{p,η}(λ,α,β) and VN_{p,η}(λ,α,β) of multivalent functions with varying arguments of coefficients. We obtain coefficients inequalities, distortion theorems and extreme points for functions in these classes. Also, we investigate several distortion inequalities involving fractional calculus. Finally, results on partial sums are considerd.

A generalized conic domain and its applications to certain subclasses of multivalent functions associated with the basic (or $ q $-) calculus

A generalized conic domain and its applications to certain subclasses of multivalent functions associated with the basic (or $ q $-) calculus

Some properties for certain subclasses of multivalent functions associated with the $$q-$$difference linear operator

Some properties for certain subclasses of multivalent functions associated with the $$q-$$difference linear operator

Coefficient inequalities for certain subclasses of multivalent functions associated with conic domain

A number of families of q-extensions of analytic functions in the open unit disk mathbb{U} have been defined by means of basic (or q-)calculus and considered from many distinctive prospectives and viewpoints. In this paper, we generalize and study certain subclasses of analytic functions involving higher-order q-derivative operators. We settle characteristic equations for these presumably new classes and also study numerous coefficient inequalities. For the results obtained in this presentation, we also carry out appropriate connections with those in multiple other concerning works on this subject.

Subclasses of p-Valent Functions Involving a New Operator Containing the Generalized Mittag–Leffler Function

The purpose of the present paper is to investigate some subordination, other properties and inclusion relations for functions in certain subclasses of multivalent functions which are defined by the linear operator containing the generalized Mittag–Leffler function.

Geometric Properties and Neighborhood for Certain Subclasses of Multivalent Functions

Geometric Properties and Neighborhood for Certain Subclasses of Multivalent Functions

Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative

In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases.

On certain subclasses of multivalent functions defined by a generalized fractional differintegral operator

The purpose of this paper is to introduce subclasses of multivalent functions by using linear operator defined by generalized fractional differintegral operator. We investigate various properties for functions of these subclasses.

Argument inequalities of certain subclass of multivalent functions defined by using new integral operator

In this paper, we introduce some interesting inequalities regarding the argument of certain p-valent functions. The subclass under investigation is defined by using certain new integral operator. Moreover, special cases and connections of the results presented here with those obtained in earlier works are pointed out.

A certain subclass of multivalent functions involving higher-order derivatives

In this paper we introduce and study a new class of analytic and p-valent functions involving higher-order derivatives. For this p-valent function class, we derive several interesting properties including (for example) coefficient inequalities, distortion theorems, extreme points, and the radii of closeto-convexity, starlikeness and convexity. Several applications involving an integral operator are also considered. Finally, we obtain some results for the modified Hadamard product of the functions belonging to the p-valent function class which is introduced here.

On certain subclasses of multivalent functions defined by multiplier transformations

Abstract The purpose of the present paper is to introduce and investigate various properties of a certain class of multivalent functions in the open unit disk defined by a multiplier transformation. In particular, we obtain some inclusion relationships and integral preserving properties of this class of functions. Relevant connections of the results presented in this paper with various known results are also pointed out. MSC:30C45.

Properties of Certain Subclass of Multivalent Functions with Negative Coefficients

Making use of a linear operator, which is defined by the Hadamard product, we introduce and study a subclassYa,c+(A,B;p,λ,α)of the classA+(p). In this paper, we obtain the coefficient inequality, distortion theorem, radius of convexity and starlikeness, neighborhood property, modified convolution properties of this class. Furthermore, an application of fractional calculus operator is given. The results are presented here would provide extensions of some earlier works. Several new results are also obtained.

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.

On Certain Subclasses of Multivalent Functions Associated with a Family of Linear Operators

Making use of a linear operator Iλp(a,c), which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion properties of these subclasses. Some radius problems are also discussed.

Generalization of Certain Subclasses of Multivalent Functions with Negative Coefficients Defined by Cho-Kwon-Srivastava Operator

Making use of the Cho-Kwon-Srivastava operator, we introduce and study a certain SCn (j, p, λ, α, δ) of p-valently analytic functions with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorem, radii of close-to-convexity, starlikeness and convexity and modified Hadamard products of functions belonging to the class SCn (j, p, λ, α, δ). Finally, several applications investigate an integral operator, and certain fractional calculus operators also considered.

Classes of multivalent functions associated with a convolution operator

We investigate several properties of the linear Aouf–Silverman–Srivastava operator and associated classes of multivalent analytic functions which were introduced and studied by Aouf et al. [M.K. Aouf, H. Silverman, H.M. Srivastava, Some families of linear operators associated with certain subclasses of multivalent functions, Comp. Math. Appl. 55 (2008) 535–549]. Several theorems are extensions of earlier results of the above paper.

Certain subclasses of multivalent functions involving linear operators

In terms of linear operators we introduce new classes of functions. Then by using differential subordinations, certain results concerning inclusion relations, coefficient bounds and other results are given.

Generalization of certain subclasses of multivalent functions with negative coefficients defined by using a differential operator

Making use of a differential operator, we introduce and study a certain class S C n ( j , p , q , α , λ ) of p -valently analytic functions with negative coefficients. In this paper, we obtain numerous sharp results including (for example ) coefficient estimates, distortion theorem, radii of close-to convexity, starlikeness and convexity and modified Hadamard products of functions belonging to the class S C n ( j , p , q , α , λ ) . Finally, several applications investigate an integral operator, and certain fractional calculus operators are also considered.

On Applications of Differential Subordination to Certain Subclass of Multivalent Functions

In the present paper, we introduce and investigate a new subclass of multivalent functions associated with the Cho-Kwon-Srivastava operator . Such results as inclusion relationships, convolution properties and criteria for starlikeness are proved. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.