Multivalent Analytic Functions Research Articles

Certain Class of <i>P</i>-Valent Analytic Function Associated with Derivative Operator and Their Properties

This study aims to define a new subclass of multivalent analytic functions in the open unit disk. Jackson's derivative operator has been used to generate this subclass. Before getting coefficient characterization, we look at certain needs for the functions related to this subclass. We can see several fascinating features, including coefficient estimates, growth and distortion theorem, extreme points, and the radius of starlikeness and convexity of functions belonging to the subclass are shown using this technique.

Applications of Fractional Calculus and Borel Distribution Series for Multivalent Functions on Complex Hilbert Space

In this paper, we introduce applications of fractional calculus techniques for a family of multivalent analytic functions defined by the Borel distribution on Hilbert space. We derive several interesting properties, including coefficient estimates, extreme points, and convex combinations.

Some Characteristics Properties for Linear Operator on Class of Multivalent Analytic Functions Defined by Differential Subordination

The purpose of this paper is to consider a linear operator and define a certain class of analytic and multivalent functions in the open unit disk associated with differential subordination. Also, we discuss some geometric properties for this class.

New Class of Multivalent Functions Defined by Generalized (p,q)-Bernard Integral Operator

Making use of the generalized $(p, q)$-Bernardi integral operator, we introduce and study a new class $\mathcal{F J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$ of multivalent analytic functions with negative coefficients in the open unit disk $E$. Several geometric characteristics are obtained, like, coefficient estimate, radii of convexity, close-to-convexity and starlikeness, closure theorems, extreme points, integral means inequalities, neighborhood property and convolution properties for functions belonging to the class $\mathcal{F} \mathcal{J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$.

New Class of Multivalent Functions Defined by Generalized (p,q)-Bernard Integral Operator

Making use of the generalized $(p, q)$-Bernardi integral operator, we introduce and study a new class $\mathcal{F J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$ of multivalent analytic functions with negative coefficients in the open unit disk $E$. Several geometric characteristics are obtained, like, coefficient estimate, radii of convexity, close-to-convexity and starlikeness, closure theorems, extreme points, integral means inequalities, neighborhood property and convolution properties for functions belonging to the class $\mathcal{F} \mathcal{J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$.

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.

Properties for Certain Class of p- Valent Functions Related to Jackson’s Operator

An inspiration from the fundamentals of (r,q) calculus to introduce an innovative subclass within the T(p) category of multivalent analytic functions, located within the confines of the open unit disk, is subjected to examination. The establishment of the subclass was achieved by employing Jackson's derivative operator to enhance the comprehension of these analytical functions. This article began by investigating and establishing adequate criteria that dictate the inclusion of functions within this recently introduced subclass. To achieve this, a comprehensive coefficient characterization to facilitate a deeper comprehension of the subclass's properties and behavior is derived. Further, various pertinent results that contribute to the broader understanding of the functions belonging to this subclass are explored. The findings and implications of these results are elucidated, underscoring the potential significance of this work in advancing the field of multivalent analytic functions and their applications. In conclusion, this paper broadens the scope of T(p) and sheds light on the distinct characteristics exhibited by the functions in this newly introduced subclass. This work sets the stage for further exploration and applications of (r,q) calculus and Jackson's derivative operator in the domain of multivalent analytic functions.

Application of subordination and superordination for multivalent analytic functions associated with differintegral operator

<abstract><p>The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on the properties of the differential subordination and superordination one of the newest techniques used in this field, we obtain some differential subordination and superordination results for multivalent functions defined by differintegral operator with $ j $-derivatives $ \Im _{p}(\nu, \rho; \ell)f(z) $ for $ \ell > 0, \ \nu, \rho \in \mathbb{R}, \ $such that $ (\rho -j)\geq 0, \nu > -\ell p\, (p\in \mathbb{N}) $ in the open unit disk $ U $. Differential sandwich result is also obtained. Also, the results are followed by some special cases and counter examples.</p></abstract>

New results and application of differential quasi subordinations for higher-order derivatives of meromorphic multivalent functions

The primary purpose of this study is to look at the differential quasi-subordination result for meromorphic multivalent analytic functions. We show how higher-order differential quasisubordination discoveries can be applied in a variety of ways in an open unit disk. We provide a new class S*p,q (x, ℓ, j). to represent higher-order derivatives of meromorphic multivalent analytic functions associated with the operator. We have some findings for this class.

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

Hadamard Product of Certain Multivalent Analytic Functions with Positive Real Parts

This paper aims to provide sufficient conditions for starlikeness and convexity of Hadamard product (convolution) of certain multivalent analytic functions with positive real parts. Moreover, the starlikeness conditions for a certain integral operator and other convolution results are also considered.

On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional differential and integral operators of a complex variable have been undertaken. (2) Methods: In this effort, we aim to present a generalization of a class of analytic functions based on a complex fractional differential operator. This class is defined by utilizing the subordination and superordination theory. (3) Results: We illustrate different fractional inequalities of starlike and convex formulas. Moreover, we discuss the main conditions to obtain sandwich inequalities involving the fractional operator. (4) Conclusion: We indicate that the suggested class is a generalization of recent works and can be applied to discuss the upper and lower bounds of a special case of fractional differential equations.

Certain Subclasses of Analytic Multivalent Functions Associated with Petal-Shape Domain

In this article, we introduce a new class of multivalent analytic functions associated with petal-shape region. Furthermore, some useful properties, such as the Fekete–Szegö inequality, and their consequences for some special cases are discussed. For some specific value of function f, we obtain sufficient conditions for multivalent starlike functions connected with petal-shape domain. Finally, in the concluding section, we draw the attention of the interested readers toward the prospect of studying the basic or quantum (or q-) generalizations of the results, which are presented in this paper. However, the (p,q)-variations of the suggested q-results will provide a relatively minor and inconsequential development because the additional (rather forced-in) parameter p is obviously redundant.

Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli

Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1<1. Several previous results are extended.

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.

A variety of multivalently analytic functions with complex coefficients and some argument properties of their applications

The principal goal of this scientific note is first to compose various rational types functions directly connecting to a variety of multivalently functions with complex coefficients, which are regular in certain domains in the complex plane, and then to designate numerous argument properties associating with certain applications of those (multivalent) functions

Sandwich Theorems for Multivalent Analytic Functions Associated with Differential Operator

The purpose of this paper is to derive subordination and superordination results involving differential operator for multivalent analytic functions in the open unit disk. These results are applied to obtain sandwich results. Our results extend corresponding previously known results.

Some New Results of Differential Subordinations for HigherOrder Derivatives of Multivalent Functions

The main purpose of this paper is to study the differential subordination result for multivalent analytic functions. We give some applications of higher-order differential subordination results involving Hadamard product for multivalent analytic functions with generalized hypergeometric function in open unit disk. We have also discussed and studied a new class of higher-order derivatives of multivalent analytic functions in open unit disk of complex plane related to linear operator and we obtain some results connected inclusion relationship, argument estimate, integral representation and subordination property. by using the method of differential subordination we aim to prove some classical results in multivalent functions theory. We obtain some interesting properties of this class and establish several strong differential subordination for higher-order derivatives of multivalent analytic functions. By making use of the principle of subordination, we introduce a new class W_(p, q)^(l, k) (η,α_1, m; h) for higher-order derivatives of multivalent analytic functions associated with Dziok-Srivastava operator. We obtain some result for this class.

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>