Subclasses Of Multivalent Analytic Functions Research Articles

On a Class of Multivalent Functions with Negative Coefficients Involving (r, q)− Calculus

In this research, we focused on presenting a novel subclass of multivalent analytic functions situated in the open unit disk, characterized by the use of Jackson’s derivative operator. Our investigation systematically establishes the requisite inclusion conditions in this class, offering detailed coefficient characterizations. The exploration encompasses an array of significant properties intrinsic to this subclass, encompassing coefficient estimates, growth and distortion theorems, identification of extreme points, and the determination of the radius of starlikeness and convexity for functions falling within this specialized category. Expanding the preliminary findings, this research extended the inquiry to delve deeper into the intriguing features and implications associated with this new subclass of multivalent analytic functions. The research concentrated the light on the nuanced intricacies of coefficient estimates, providing a comprehensive understanding of how these functions evolve within the open unit disk through exploring the growth and distortion theorems, unraveling the underlying mathematical principles governing the behavior of functions in this subclass as they extend beyond the unit disk. The findings of this research contribute to the broader understanding of multivalent analytic functions, paving the way for further exploration and applications in diverse mathematical contexts.

On Certain Classes of Multivalent Analytic Functions Defined with Higher-Order Derivatives

This paper examines two subclasses of multivalent analytic functions defined with higher-order derivatives. These classes of functions are generalizations of several known subclasses that have been studied in separate works. Moreover, we find several interesting results for functions in these classes, including subordination results, containment relations, and integral preserving properties.

Properties of neighborhood for certain classes associated with complex order and m-q-p-valent functions with higher order

In this paper, by using q-calculus (Jackson’s q-derivative) D_{q,p} we defined new operator D_{lambda ,q,p}^{n}f^{(m)}(z). After that, we used this operator to introduce two new subclasses of multivalent analytic functions with complex order. Also, we obtained coefficients estimates and consequent inclusion relationships involving the N_{j,delta ,m}^{p,q}(f)-neighborhood of these classes

A Certain Subclass of Multivalent Analytic Functions Defined by the q-Difference Operator Related to the Janowski Functions

A class of p-valent analytic functions is introduced using the q-difference operator and the familiar Janowski functions. Several properties of functions in the class, such as the Fekete–Szegö inequality, coefficient estimates, necessary and sufficient conditions, distortion and growth theorems, radii of convexity and starlikeness, closure theorems and partial sums, are discussed in this paper.

Certain properties of multivalent analytic functions defined by $ q $-difference operator involving the Janowski function

<abstract> A new subclass of multivalent analytic functions is defined by means of $ q $-difference operator and Janowski function. Some properties of functions in this new subclass such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radii of starlikeness and convexity, partial sums and closure theorems are studied. </abstract>

Subclasses of Multivalent Analytic Functions Associated with a q-Difference Operator

In this article we introduced and studied some inclusion properties for new subclasses of multivalent analytic functions defined by using the q-derivative operator. With the aid of the Jackson q-derivative we defined two new operators that generalize many other previously studied operators, and help us to define two new subclasses of functions with several interesting properties studied in this paper. The methods used for the proof of our results are special tools of the differential subordination theory of one-variable functions.

Inclusion and properties neighbourhood for certain p-valent functions associated with complex order and q–p-valent Cătaş operator

Here in our paper, we present two new subclasses of multivalent analytic functions and complex order by using q–p-valent Cătaş operator. Also we obtain coefficient estimates and consequent inclusion relationships involving the -neighbourhood of these classes.

Some geometric properties of a subclass of multivalent analytic functions defined by the first-order differential subordination

A new class Tn(A,B,?) of multivalent analytic functions defined by the first-order differential subordination is introduced. Some geometric properties of this new class are investigated. The sharp lower bound on |z| = r &lt; 1 for the functional Re {(1-?) f(z)/zp + ?f'(z)/pzp-1} over the class Tn(A,B,0) is given.

A Certain Subclass of Multivalent Analytic Functions with Negative Coefficients for Operator on Hilbert Space

In the present work, we introduce and study a certain subclass for multivalent analytic functions with negative coefficients defined on complex Hilbert space. We establish a number of geometric properties, like, coefficient estimates, convex set, extreme points and radii of starlikeness and convexity.

Subordination and inclusion theorems for higher order derivatives of a generalized fractional differintegral operator

The main object of this paper is to investigate some subordination results of certain subclasses of multivalent analytic functions which are defined by a generalized fractional differintegral operator. Inclusion relations for functions in the class mathcal {S}_{p,q}^{lambda,mu,eta }left (zeta ;A,Bright) and the images of these functions by the generalized Bernardi-Libera-Livingston integral operator are also considered.

Some Geometric Properties of Multivalent Functions Defined on Hilbert Space

The main goal of this paper is to study applications of the fractional calculus techniques for a certain subclass of multivalent analytic functions on Hilbert Space. Also, we obtain the coefficient estimates, extreme points, convex combination and hadamard product.

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 subclass of p-valent analytic functions associated with differintegral operator

In this paper, by making use of the fractional differintegral operator, we introduce a certain subclass of multivalent analytic functions. We study some properties such as inclusion relationship, integral preserving, convolution and some interesting results for multivalent starlikeness are proved.

Some Applications of Differential Subordination of p-Valent Functions

Abstract The object of the present paper is to investigate some inclusion relationships and a number of other properties of several subclasses of multivalent analytic functions, which are defined here by using the hypergeometric function. Relevant connections of the results presented here with those obtained in earlier works are pointed out.

On Certain Subclasses of Multivalent Analytic Functions with Complex Order Involving a Linear Operator

In the present investigation, we introduce a class \(\mathcal {R}_{p}^{b}(a,c,A,B)\) of multivalent analytic functions with complex order, by using a linear operator. For this class, a sufficient condition in terms of the coefficients is obtained, the Fekete–Szego problem and determination of sharp upper bound for the second Hankel determinant is completely solved. We also find the radii of starlikeness and convexity for certain subclass of \(\mathcal {R}_{p}^{b}(a,c,A,B)\). Relevant connections of the results presented here with those obtained in earlier works are pointed out.

On a certain subclass of multivalent analytic functions associated with a generalized fractional differintegral operator

On a certain subclass of multivalent analytic functions associated with a generalized fractional differintegral operator

Certain Subclasses of Multivalent Analytic Functions Involving Linear Operator

Certain Subclasses of Multivalent Analytic Functions Involving Linear Operator

Subordination properties of multivalent functions involving an extended fractional differintegral operator

The object of this article is to investigate inclusion, radius, and other various properties of subclasses of multivalent analytic functions, which are defined by using an extended version of the Owa-Srivastava fractional differintegral operator Ω(λ, p).

Subordination Properties of Multivalent Functions Defined by Generalized Multiplier Transformation

The main object of the present paper is to investigate several interesting subordination properties and a sharp inclusion relationship for certain subclass of multivalent analytic functions, which are defined here by the generalized multiplier transformation. Relevant connections of the results which are presented in this paper with various known results are also considered.

A Certain Subclass of Multivalent Analytic Functions Defined by Fractional Calculus Operator

In this paper we introduce a new subclass of multivalent analytic functions defined by fractional calculus operator. Such results as subordination and superordination properties, convolution properties, inequality properties and other interesting properties of this subclass are proved.