Univalent Analytic Functions Research Articles

3rd-Order Differential Subordination and Superordination Results for Univalent Analytic Functions Associated with Zeta-Riemann Fractional Differential Operator

Using the results of 3rd order differential subordination, we introduce certain families of admissible functions and discuss some applications of 3rd order differential subordination for normalized analytic functions associated with novel fractional operator namely Zeta-Riemann Fractional differential operator. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted.

A New Sandwich Theorem Relating to the Generalized Integral Operator for Univalent Analytic Functions

A New Sandwich Theorem Relating to the Generalized Integral Operator for Univalent Analytic Functions

On the Fekete–Szegö Problem for Certain Classes of (γ,δ)-Starlike and (γ,δ)-Convex Functions Related to Quasi-Subordinations

In the present paper, we propose new generalized classes of (p,q)-starlike and (p,q)-convex functions. These classes are introduced by making use of a (p,q)-derivative operator. There are established Fekete–Szegö estimates |a3−μa22| for functions belonging to the newly introduced subclasses. Certain subclasses of analytic univalent functions associated with quasi-subordination are defined.

A New Class of Univalent Functions Defined by Differential Operator

In the present work, we submit and study a new class $\mathcal{S}_{\lambda, \alpha, b}^{z, m, t}(\beta, \gamma, \omega, \mu)$ containing analytic univalent functions defined by new differential operator $D_{\lambda, \alpha}^{z, m, t}$ in the open unit disk $E=\{s \in \mathbb{C}:|s|<1\}$. We get some geometric properties, such as, coefficient estimate, growth and distortion theorems, convex set, radii of convexity and starlikeness, weighted mean, arithmetic mean and partial sums for functions belonging to the class $\mathcal{S}_{\lambda, \alpha, b}^{z, m, t}(\beta, \gamma, \omega, \mu)$.

On a Class of Analytic Univalent Functions Associated with (H-R) Fractional Derivative

In this paper, we introduced a class of analytic functions defined by (H–R) fractional derivative defined in the unit disk, we obtained coefficient bounded, so we obtained some theorems of this class. 2000Mathematics Subject classification: 30C45.

Hankel determinants, Fekete-Szegö inequality, and estimates of initial coefficients for certain subclasses of analytic functions

<abstract><p>In this paper, we define new subclasses of analytic functions related to a modified sigmoid function and analytic univalent function. Then, we attempt to investigate the upper bounds of the third and fourth Hankel determinant in the special case. Further, bound on third Hankel determinant of its inverse function is also investigated. In addition, we attempt to obtain the Fekete-Szegö inequality for the classes. Then, we estimate the bounds of initial coefficients for the function belongs to some kind of new subclasses when its inverse function also belongs to these new subclasses.</p></abstract>

Applications of Subordination for Holomorphic Functions Stated by Generalized By‐Product Operator

The aim of this research is to investigate certain problems of differential subordination and superordination of analytic univalent functions in an open unit disk. Furthermore, the universal by‐product operator and geometric properties such as coefficient inequalities are investigated. Remarkable results on the differential subordination and superordination of analytic univalent functions and results using higher derivative operator for differential subordination are obtained. Some interesting applications of subordination in the unit disk are obtained using convolution and convexity.

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.

Univalence Criteria for Locally Univalent Analytic Functions

Univalence Criteria for Locally Univalent Analytic Functions

Concerning a Novel Integral Operator and a Specific Category of Starlike Functions

In this study, a novel integral operator that extends the functionality of some existing integral operators is presented. Specifically, the integral operator acts as the inverse operator to the widely recognized Opoola differential operator. By making use of the integral operator, a certain subclass of analytic univalent functions defined in the unit disk is proposed and investigated. This new class encompasses some familiar subclasses, like the class of starlike and the class of convex functions, while some new ones are introduced. The investigation thereafter covers coefficient inequality, distortion, growth, covering, integral preserving, closure, subordinating factor sequence, and integral means properties. Furthermore, the radii problems associated with this class are successfully addressed. Additionally, a few remarks are provided, to show that the novel integral operator and the new class generalize some existing ones.

On Third-Order Differential Subordinations and Superordinations Results for Univalent Analytic Functions Defined by a New Operator

Abstract: In the current paper, we obtain sandwich theorems for univalent functions by using some of the finding of Third-order differential subordination and superordination for univalent functions defined by a new operator .

An exact estimate of the third Hankel determinants for functions inverse to convex functions

Invesigation of bounds for Hankel determinat of analytic univalent functions is prominent intrest of many researcher from early twenth century to study geometric properties. Many authors obtained non sharp upper bound of third Hankel determinat for different subclasses of analytic univalent functions until Kwon et al. obtained exact estimation of the fourth coefficeient of Caratheodory class. Recently authors made use of an exact estimation of the fourth coefficient, well known second and third coefficient of Caratheodory class obtained sharp bound for the third Hankel determinant associated with subclasses of analytic univalent functions. Let $w=f(z)=z+a_{2}z^{2}+\cdots$ be analytic in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$, and $\mathcal{S}$ be the subclass of normalized univalent functions with $f(0)=0$, and $f'(0)=1$. Let $z=f^{-1}$ be the inverse function of $f$, given by $f^{-1}(w)=w+t_2w^2+\cdots$ for some $|w|<r_o(f)$. Let $\mathcal{S}^c\subset\mathcal{S}$ be the subset of convex functions in $\mathbb{D}$. In this paper, we estimate the best possible upper bound for the third Hankel determinant for the inverse function $z=f^{-1}$ when $f\in \mathcal{S}^c$.Let $\mathcal{S}^c$ be the class of convex functions. We prove the following statements (Theorem):If $f\in$ $\mathcal{S}^c$, then\begin{equation*}\big|H_{3,1}(f^{-1})\big| \leq \frac{1}{36}\end{equation*} and the inequality is attained for $p_0(z)=(1+z^3)/(1-z^3).$

Investigation of the Hankel Determinant Sharp Bounds for a Specific Analytic Function Linked to a Cardioid-Shaped Domain

One of the challenging tasks in the study of function theory is how to obtain sharp estimates of coefficients that appear in the Taylor–Maclaurin series of analytic univalent functions, and for obtaining these bounds, researchers used the concepts of Carathéodory functions. Among these coefficient-related problems, the problem of the third-order Hankel determinant sharp bound is the most difficult one. The aim of the present study is to determine the sharp bound of the Hankel determinant of third order by using the methodology of the aforementioned Carathéodory function family. Further, we also study some other coefficient-related problems, such as the Fekete–Szegő inequality and the second-order Hankel determinant. We examine these results for the family of bounded turning functions linked with a cardioid-shaped domain.

New Results about Fuzzy Differential Subordinations Associated with Pascal Distribution

Based upon the Pascal distribution series Nq,λr,mΥ(ζ):=ζ+∑j=m+1∞j+r−2r−11+λ(j−1)qj−1(1−q)rajζj, we can obtain a set of fuzzy differential subordinations in this investigation. We also newly obtain class Pq,λF,r,mη of univalent analytic functions defined by the operator Nq,λr,m, give certain properties for the class Pq,λF,r,mη and also obtain some applications connected with a special case for the operator. New research directions can be taken on fuzzy differential subordinations associated with symmetry operators.

Inclusion Properties of p-Valent Functions Associated with Borel Distribution Functions

In this paper, we define a differential operator on an open unit disk Δ by using the novel Borel distribution (BD) operator and means of convolution. This operator is adopted to introduce new subclasses of p-valent functions through the principle of differential subordination, and we focus on some interesting inclusion relations of these classes. Additionally, some inclusion relations are derived by using the Bernardi integral operator. Moreover, relevant convolution results are established for a class of analytic functions on Δ, and other results of analytic univalent functions are derived in detail. This study provides a new perspective for developing p-univalent functions with BD and offers valuable understanding for further research in complex analysis.

Univalence criteria for locally univalent analytic functions

UDC 517.5 Suppose that p ( z ) = 1 + z ϕ ' ' ( z ) / ϕ ' ( z ) , where ϕ ( z ) is a locally univalent analytic function in the unit disk D with ϕ ( 0 ) = ϕ ' ( 1 ) - 1 = 0. We establish the lower and upper bounds for the best constants σ 0 and σ 1 such that e - σ 0 / 2 < | p ( z ) | < e σ 0 / 2 and | p ( w ) / p ( z ) | < e σ 1 for z , w ∈ D , respectively, imply the univalence of ϕ ( z ) in D .

Some Subclasses of q-Analytic Starlike Functions

We define two new subclasses, $\mathcal{S}_{q}^{\ast }(\alpha )$ and $\mathcal{TS}_{q}^{\ast }(\alpha )$, of analytic univalent functions. We obtain a sufficient condition for analytic univalent functions to be in $\mathcal{S}_{q}^{\ast }(\alpha )$ and we prove that this condition is also necessary for the functions in the class $\mathcal{TS}_{q}^{\ast }(\alpha )$. We also obtain extreme points, distortion bounds, covering result, convex combination and convolution properties for the functions in the class $\mathcal{TS}_{q}^{\ast }(\alpha )$.

Third-Order Differential Subordination and Superordination Results for Analytic Univalent Functions Using Hadamard Product Operator

In this paper, we aim to obtain some results of third-order of differential subordination and superordination with sandwich theorems for analytic univalent functions using the operator Some new results has been introduced.

Fuzzy differential subordinations connected with convolution

"The object of the present paper is to obtain several fuzzy differential subordinations associated with Linear operator $$\mathcal{D}_{n,\delta ,g}^{m}f(z) =z+\sum\limits_{j=2}^{\infty }\left[ 1+\left( j-1\right) c^{n}(\delta )\right] ^{m}a_{j}b_{j}z^{j}.$$ Using the operator $\mathcal{D}_{n,\delta ,g}^{m},$ we also introduce a class $\mathcal{H}_{n,m,\delta }^{F}\left( \eta ,g\right) $ of univalent analytic functions for which we give some properties."

An Application of the Prabhakar Fractional Operator to a Subclass of Analytic Univalent Function

Fractional differential operators have recently been linked with numerous other areas of science, technology and engineering studies. For a real variable, the class of fractional differential and integral operators is evaluated. In this study, we look into the Prabhakar fractional differential operator, which is the most applicable fractional differential operator in a complex domain. In terms of observing a group of normalized analytical functions, we express the operator. In the open unit disc, we deal with its geometric performance. Applying the Prabhakar fractional differential operator dcθα,βγ,ω to a subclass of analytic univalent function results in the creation of a new subclass of mathematical functions: W(γ,ω,α,β,θ,m,c,z,p,q). We obtain the characteristic, neighborhood and convolution properties for this class. Some of these properties are extensions of defined results.