Univalent Functions Research Articles

Class of Meromorphic Univalent Functions with Fixed Second Positive Coefficients Defined by q-Difference Operator

In this paper using a q-difference operator, a class of meromorphic univalent functions with fixed second positive coefficients is defined. Coefficient estimates, some distortion theorems and other properties for this class are obtained. Various results obtained are sharp.

A note on differences of composition operators acting on the Hardy space

When $\varphi$ and $\psi$ are holomorphic self-maps of the unit disk with bounded multiplicity, we give a compact characterization for the difference of composition operators $C_\varphi $ and $C_\psi $ acting on the Hardy space, which extends a recent result in the case of univalent maps by Choe et al.

Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range Cn

In this paper we study the class of ``shearing'' holomorphic maps of the unit ball of the form $(z,w)\mapsto (z+g(w), w)$. Besides general properties, we use such maps to construct an example of a normalized univalent map of the ball onto a Runge domain in $\C^n$ which however cannot be embedded into a Loewner chain whose range is $\C^n$.

Convergence of a Godunov scheme for degenerate conservation laws with BV spatial flux and a study of Panov-type fluxes

We prove the convergence of the Godunov-type scheme for a scalar conservation law in one space dimension with possibly infinitely many spatial discontinuities, which may have accumulation points. In contrast to the study appearing in Ghoshal, Jana and Towers [Convergence of a Godunov scheme to an Audusse–Perthame adapted entropy solution for conservation laws with BV spatial flux, Numer. Math. 146(3) (2020) 629–659], we do not restrict the flux to be unimodal and allow for the case where the flux has degeneracies due to which the corresponding singular map may not be invertible and hence, the so-called singular mapping technique is not applicable. We present two proofs of convergence depending on the nature of the flux. For fluxes which are piecewise constant in the space variable, convergence is established by proving [Formula: see text] bounds on the finite volume approximations away from the set of spatial discontinuity. On the other hand, if the fluxes are of Panov-type, i.e. [Formula: see text], we prove the convergence by establishing a novel [Formula: see text] property, which in turn implies the existence of [Formula: see text] bounds on the solution. We present numerical examples that illustrate the theory.

Volterra-Type Operators on the Subclasses of Univalent Functions

Volterra-Type Operators on the Subclasses of Univalent Functions

On a subclass of meromorphic functions with positive coefficients defined by rapid operator

In this paper, we introduce and study a new subclass of meromorphic univalent functions defined by Rapid operator. We obtain coefficient inequalities, extreme points, radius of starlikeness and convexity. Finally we obtain partial sums and neighborhood properties for the class ∑*p(γ,κ,μ,θ)

Some Subclasses of Univalent Functions Associated with the k-Ruscheweyh Derivative Operator

Some Subclasses of Univalent Functions Associated with the k-Ruscheweyh Derivative Operator

Some Properties of a Family of Univalent Functions Defined by a Generalized Opoola Differential Operator

Abstract In this investigation, we introduce a new q-differential operator that generalizes the well-known Opoola differential operator. Using the operator, we define a family of q-bounded turning functions. The new class is denoted by ℛ q n (µ, β, τ ; λ). Afterwards, inclusion, characterisation, growth, distortion, covering, linear combination and neighborhood properties of functions f ∈ ℛ q n (µ, β, τ ; λ) are presented.

The Sharp Bounds of Hankel Determinants for the Families of Three-Leaf-Type Analytic Functions

The theory of univalent functions has shown strong significance in the field of mathematics. It is such a vast and fully applied topic that its applications exist in nearly every field of applied sciences such as nonlinear integrable system theory, fluid dynamics, modern mathematical physics, the theory of partial differential equations, engineering, and electronics. In our present investigation, two subfamilies of starlike and bounded turning functions associated with a three-leaf-shaped domain were considered. These classes are denoted by BT3l and S3l*, respectively. For the class BT3l, we study various coefficient type problems such as the first four initial coefficients, the Fekete–Szegö and Zalcman type inequalities and the third-order Hankel determinant. Furthermore, the existing third-order Hankel determinant bounds for the second class will be improved here. All the results that we are going to prove are sharp.

On Estimates of Some Coefficient Functionals for Certain Meromorphic Univalent Functions

On Estimates of Some Coefficient Functionals for Certain Meromorphic Univalent Functions

Upper bound on the third hankel determinant for the class of univalent functions using an integral operator

Upper bound on the third hankel determinant for the class of univalent functions using an integral operator

On Sandwich-Type Results for a Subclass of Certain Univalent Functions Using a New Hadamard Product Operator

This paper is concerned with studying some results by introducing a new Hadamard product Mγ,b,v,δC,η operator for differential subordination and superordination for certain univalent functions in the open unit disc U. Firstly, we state some basic definitions and required theorems. Furthermore. Some sandwich theorems are derived. The differential subordination theory’s features and outcomes are symmetric to those derived using the differential superordination theory.

Harmonic spirallike functions and harmonic strongly starlike functions

In this note, we define two subclasses of normalized harmonic univalent functions of the unit disk, spirallike functions and strongly starlike functions, which preserve a hereditary property and have nice analytic and geometric characterizations. We also investigate the uniform boundedness and quasiconformal extendability of strongly starlike functions. Some coefficient conditions can be given for strong starlikeness and spirallikeness. We consider a special form of harmonic functions as an application.

On Subclasses of Uniformly Convex Spriallike Function Associated with Poisson Distribution Series

Geometric Function Theory is one of the major area of mathematics which suggests the significance of geometric ideas and problems in complex analysis. Recently, the univalent functions are given particular attention and they are used to construct linear operators that preserve the class of univalent functions and some of its subclasses. Also, similar attention has been given to distribution series. Many authors have studied about certain subclasses of univalent and bi-univalent functions connected with distribution series like Pascal distribution, Binomial distribution, Poisson distribution, Mittag-Leffler-type Poisson distribution, Geometric distribution, Exponential distribution, Borel distribution, Generalized distribution and Generalized discrete probability distribution to name few. Some of the important results on Uniformly convex spirallike functions (UCF) and Uniformly spirallike functions (USF) related with such a distribution series are also of interest. The main aim of the present investigation is to obtain the necessary and sufficient conditions for Poisson distribution series to belong to the classes <img src=image/13427077_01.gif> and <img src=image/13427077_02.gif>. The inclusion properties associated with Poisson distribution series are taken up for study in this article. Proof of some inequalities on integral function connected to Poisson distribution series has also been discussed. Further, some corollaries and results that follow consequently from the theorems are also analysed.

The Radii of Starlikeness for Concave Functions

Let <img src=image/13426735_02.gif> denote the functions' class that is normalized, analytic, as well as univalent in the unit disc given by <img src=image/13426735_01.gif>. Convex, starlike, as well as close-to-convex functions resemble the main subclasses of <img src=image/13426735_02.gif>, expressed by <img src=image/13426735_03.gif>, as well as <img src=image/13426735_04.gif>, accordingly. Many mathematicians have recently studied radius problems for various classes of functions contained in <img src=image/13426735_02.gif>. The determination of the univalence radius, starlikeness, and convexity for specific special functions in <img src=image/13426735_02.gif> is a relatively new topic in geometric function theory. The problem of determining the radius has been initiated since the 1920s. Mathematicians are still very interested in this, particularly when it comes to certain special functions in <img src=image/13426735_02.gif>. Indeed, many papers investigate the radius of starlikeness for numerous functions. With respect to the open unit disc <img src=image/13426735_05.gif> and class <img src=image/13426735_02.gif>, the class of concave functions <img src=image/13426735_06.gif>, known as <img src=image/13426735_07.gif>, is defined. It is identified as a normalised analytic function <img src=image/13426735_08.gif>, which meets the requirement of having the opening angle of <img src=image/13426735_09.gif> at <img src=image/13426735_10.gif>. A univalent function <img src=image/13426735_11.gif> is known as concave provided that <img src=image/13426735_12.gif> is concave. In other words, we have that <img src=image/13426735_13.gif> is also convex. There is no literature to date on determining the radius of starlikeness for concave univalent functions related to certain rational functions, lune, cardioid, and the exponential equation. Hence, by employing the subordination method, we present new findings on determining several radii of starlikeness for different subclasses of starlike functions for the class of concave univalent functions <img src=image/13426735_07.gif>.

On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions

In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk. The main tools for our discussions were the Kudriasov conditions for the univalency of functions, as well as functional inequalities for the generalized Bessel functions. We included the conditions for the univalency of integral operators that involve Bessel, modified Bessel and spherical Bessel functions as special cases. Furthermore, we provided sufficient conditions for the integral operators that involve trigonometric, as well as hyperbolic, functions as an application of our results.

Q-Analogue of New Subclass of Salagean-type Harmonic Univalent Functions defined by Subordination

We introduce and investigate q-analogue of a new subclass of Salagean-type harmonic univalent functions defined by subordination. We first obtained a coefficient characterization of these functions. We give necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for this subclass of harmonic univalent functions with negative coefficients.

Q-Analogue of a New Subclass of Harmonic Univalent Functions Associated with Subordination

In this article, we introduce and investigate the q-analogue of a new subclass of harmonic univalent functions defined by subordination. We first obtain a coefficient characterization of these functions. We give compactness and extreme points, distortion bounds, necessary and sufficient convolution conditions for this subclass of harmonic univalent functions with negative coefficients. The symmetry properties and other properties of the q-analogue subclass of functions presented in this paper shed light on future studies.

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.

Applications of Fractional Calculus on a Certain Class of Univalent Functions Associated with Wanas Operator

The purpose of this work is to use fractional integral and Wanas operator to define a certain class of analytic and univalent functions defined in the open unit disk U. Also, we obtain some results for this class such as integral representation, inclusion relationship and argument estimate.