Family Of Analytic Functions Research Articles

Applications of Generalized Hypergeometric Distribution on Comprehensive Families of Analytic Functions

A sequence of n trials from a finite population with no replacement is described by the hypergeometric distribution as the number of successes. Calculating the likelihood that factory-produced items would be defective is one of the most popular uses of the hypergeometric distribution in industrial quality control. Very recently, several researchers have applied this distribution on certain families of analytic functions. In this study, we provide certain adequate criteria for the generalized hypergeometric distribution series to be in two families of analytic functions defined in the open unit disk. Furthermore, we consider an integral operator for the hypergeometric distribution. Some corollaries will be implied from our main results.

Coefficient Bounds for q-Noshiro Starlike Functions in Conic Region

We present and examine a new family of analytic functions that can be described by a q-Ruscheweyh differential operator. We discuss several novel results, including coefficient inequalities and other noteworthy properties such as partial sums and radii of starlikeness. Moreover, coefficient estimates for the class of Janowski starlike functions associated with symmetric conic domains are also discussed.

Connections between normalized Wright functions with families of analytic functions

We establish sufficient conditions for normalized Wright functions to be in certain subclasses of analytic univalent functions in the unit disc U. Furthermore, we examine some geometric properties of integral transforms involving normalized Wright functions.

Studies on a new K-symbol analytic functions generated by a modified K-symbol Riemann-Liouville fractional calculus

Analytic functions are very helpful in many mathematical and scientific uses, such as complex integration, potential theory, and fluid dynamics, due to their geometric features. Particularly conformal mappings are widely used in physics and engineering because they make it possible to convert complex physical issues into simpler ones with simpler answers. We investigate a novel family of analytic functions in the open unit disk using the K-symbol fractional differential operator type Riemann-Liouville fractional calculus of a complex variable. For the analysis and solution of differential equations containing many fractional orders, it offers a potent mathematical framework. There are ongoing determinations to strengthen the mathematical underpinnings of K-symbol fractional calculus theory and investigate its applications in various fields.•Normalization is presented for the K-symbol fractional differential operator. Geometric properties are offered of the proposed K-symbol fractional differential operator, such as the starlikeness property and hence univalency in the open unit disk.•The formula of the Alexander integral involving the proposed operator is suggested and studied its geometric properties such as convexity.•Examples are illustrated to fit our pure result. Here, the technique is based on the concepts of geometric function theory in the open unit disk, such as the subordination and Jack lemma.

Coefficient Inequalities of q-Bi-Univalent Mappings Associated with q-Hyperbolic Tangent Function

The present study introduces a new family of analytic functions by utilizing the q-derivative operator and the q-version of the hyperbolic tangent function. We find certain inequalities, including the coefficient bounds, second Hankel determinants, and Fekete–Szegö inequalities, for this novel family of bi-univalent functions. It is worthy of note that almost all the results are sharp, and their corresponding extremal functions are presented. In addition, some special cases are demonstrated to show the validity of our findings.

Family of Analytic Functions with Negative Coefficients Involving $q-$Analogue of Multiplier Transformation Operator

We introduce a new class of analytic functions with negative coefficients by using the $q-$analogue of multiplier transformation operator. Coefficient inequalities, distortion theorems, closure theorems, and some properties involving the modified Hadamard products, radii of close-to-convexity, starlikeness, and convexity, and integral operators associated with functions belonging to this class are obtained.

Semigroups of composition operators on Hardy spaces of Dirichlet series

We consider continuous semigroups of analytic functions {Φt}t≥0 in the so-called Gordon-Hedenmalm classG, that is, the family of analytic functions Φ:C+→C+ giving rise to bounded composition operators in the Hardy space of Dirichlet series H2. We show that there is a one-to-one correspondence between continuous semigroups {Φt}t≥0 in the class G and strongly continuous semigroups of composition operators {Tt}t≥0, where Tt(f)=f∘Φt, f∈H2. We extend these results for the range p∈[1,∞). For the case p=∞, we prove that there is no non-trivial strongly continuous semigroup of composition operators in H∞. We characterize the infinitesimal generators of continuous semigroups in the class G as those Dirichlet series sending C+ into its closure. Some dynamical properties of the semigroups are obtained from a description of the Koenigs map of the semigroup.

Inequalities for the Coefficients of Schwarz Functions

The relation between a considered family of analytic functions and the class {mathcal {P}} of functions with a positive real part is one of the main tools used in solving various extremal problems, among others coefficient problems. Another approach can be useful in solving such tasks. This approach is to exploit the correspondence between a considered family and the family {mathcal {B}}_0 of bounded analytic functions omega such that omega (0)=0. Such functions appear in the well-known Schwarz lemma, so they are called Schwarz functions. In the literature, there are numerous coefficient functionals discussed for functions in {mathcal {P}}. On the other hand, relative functionals for functions in {mathcal {B}}_0 are not so commonly studied. Consequently, we do not know so much about coefficient inequalities for Schwarz functions. We shall fill the gap to some extent considering two types of functionals. The first one is a Zalcman-type functional c_{n}-c_{k}c_{n-k}; the other one is the Hankel determinant c_{n-1}c_{n+1}-c_{n}{}^2. For these functionals, bounds with respect to a fixed first coefficient c_1 (or a few initial coefficients) are obtained. Some generalizations of these functionals are also given. All results are sharp.

Estimate of third Hankel determinant for a subfamily of analytic functions

Abstract In this article, our aim is to study analytic functions related with Salagean operator and associated with the right half of the lemniscate of Bernoulli. We find the estimates of the third Hankel determinant for new family of analytic functions. It is important to mention that our results generalize a number of existence results in the literature.

On a Subfamily of q-Starlike Functions with Respect to m-Symmetric Points Associated with the q-Janowski Function

The main objective of this paper is to study a new family of analytic functions that are q-starlike with respect to m-symmetrical points and subordinate to the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego functional |a3−μa22| and convolution properties for the functions belonging to this new class. Several consequences of main results are also obtained.

Coefficient Estimates for Certain Families of Analytic Functions Associated with Faber Polynomial

In this paper, we use the Faber polynomial expansion to obtain bounds for the general coefficients a n of bi-univalent functions in the family of analytic functions in the open unit disk. Estimation of the bound value for the initial coefficients of the functions in these classes is also established.

On a New Subclass of q-Starlike Functions Defined in q-Symmetric Calculus

Geometric function theory combines geometric tools and their applications for information and communication analysis. It is also successfully used in the field of advanced signals, image processing, machine learning, speech and sound recognition. Various new subclasses of analytic functions have been defined using quantum calculus to investigate many interesting properties of these subclasses. This article defines a new class of q-starlike functions in the open symmetric unit disc ∇ using symmetric quantum calculus. Extreme points for this class as well as coefficient estimates and closure theorems have been investigated. By fixing several coefficients finitely, all results were generalized into families of analytic functions.

Brief Study on a New Family of Analytic Functions

Brief Study on a New Family of Analytic Functions

Strong Differential Sandwich Results for Analytic Functions Associated with Wanas Differential Operator

In this article, we introduce and study two new families of analytic functions by using strong differential subordinations and superordinations associated with Wanas differential operator/. We also give and establish some important properties of these families.

Certain Analytic Functions Defined by Generalized Mittag-Leffler Function Associated with Conic Domain

In the present paper, we investigate and introduce several properties of certain families of analytic functions in the open unit disc, which are defined byq-analogue of Mittag-Leffler function associated with conic domain. A number of coefficient estimates of the functions in these classes have been obtained. Sufficient conditions for the functions belong to these classes are also considered.

Connections between normalized Wright functions with families of analytic functions with negative coefficients

Abstract In this article we present sufficient conditions that ensures that normalized Wright functions belong to certain subclasses of analytic univalent functions with negative coefficients in the unit disc 𝒰 {\mathcal{U}} . We also provide some geometric properties of integral transforms involving normalized Wright functions.

Non-extreme-Points Approach to Extreme Points of Integral Families of Analytic Functions

Non extreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a 2-parameter collection of kernel functions integrated against measures on the torus. Families from classical geometric function theory such as the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others are included. However for these families of analytic functions, identifying “all” the extreme points remains a difficult challenge except in some special cases. Aharonov and Friedland [1] identified a band of points on the unit circle which corresponds to the set of extreme points for these 2-parameter collections of kernel functions. Later this band of extreme points was further extended by introducing a new technique by Dow and Wilken [3]. On the other hand, a technique to identify a non extreme point was not investigated much in the past probably because identifying non extreme points does not directly help solving the optimization of linear extremal problems. So far only one point on the unit circle has beenidentified which corresponds to a non extreme point for a 2-parameter collections of kernel functions. This leaves a big gap between the band of extreme points and one non extreme point. The author believes it is worth developing some techniques, and identifying non extreme points will shed a new light in the exact determination of the extreme points. The ultimate goal is to identify the point on the unit circle that separates the band of extreme points from non extreme points. The main result introduces a new class of non extreme points.

On Quantum Differential Subordination Related with Certain Family of Analytic Functions

Recently, there is a rapid increase of research in the area of Quantum calculus (known as q -calculus) due to its widespread applications in many areas of study, such as geometric functions theory. To this end, using the concept of q -conic domains of Janowski type as well as q - calculus, new subclasses of analytic functions are introduced. This family of functions extends the notion of α -convex and quasi-convex functions. Furthermore, a coefficient inequality, sufficiency criteria, and covering results for these novel classes are derived. Besides, some remarkable consequences of our investigation are highlighted.

Sandwich weighted composition operators between some families of analytic functions

In this paper, we characterize the boundedness and compactness of sandwich weighted composition operators between some analytic function spaces and Bloch and little Bloch-type spaces. We also compute upper and lower bounds for the norm of sandwich weighted composition operators.

The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator

A useful family of fractional derivative and integral operators plays a crucial role on the study of mathematics and applied science. In this paper, we introduce an operator defined on the family of analytic functions in the open unit disk by using the generalized fractional derivative and integral operator with convolution. For this operator, we study the subordination-preserving properties and their dual problems. Differential sandwich-type results for this operator are also investigated.