Class Of Univalent Research Articles

On a subclass of close-to-convex functions

In this paper, we define a new subclass of close-to-convex functions with respect to certain univalent functions studied by [Z. Peng and G. Zhong, Some properties for certain classes of univalent functions defined by differential inequalities, Acta Math. Sci. Ser. B (Engl. Ed.) 37(1) (2017) 69–78]. We find certain examples of functions belong to the class. Further, we give coefficient estimates, distortion theorem and some more results for this new subclass. Finally, we obtain radius of convexity for functions belong to the class.

Classes of univalent functions having fixed point

Classes of univalent functions having fixed point

Coefficient Bounds of Bi-Univalent Function Involving Pseudo-Starlikeness Associatedwith Sigmoid Function Defined by Salagean Operator via Chebyshev Polynomial

Some special classes of univalent functions play an important role in geometric function theory because of their geometric properties. Many of such classes have been introduced and studied; some became well known, for example, the classes of convex, starlike, close to convex, strongly convex and strongly starlike functions. Previous studies by Awolere and Oladipupo (2018) now served as motivation and background to investigate certain classes of analytic, univalent and bi-univalent functions in terms of their coefficient bounds involving salagean and sigmoid functions via Chebyshev poynomial. The classes 퐻푛(휆,훽,훾(푠),휙(푧,푡))are newly established classes for which coefficient bounds will be determined. The aim of the present work is to investigate coefficient bound for class 퐻푛(휆,훽,훾(푠),휙(푧,푡))of pseudo-starlikeness associated with sigmoid functions defined by Salagean operator via Chebyshev polynomial, Fekete-szego problem will also be established and the Hankel of the function will be determined

Harmonic analogue of Bohr phenomenon of certain classes of univalent and analytic functions

A class $ \mathcal {F} $ consisting of analytic functions $ f(z)=\sum _{n=0}^{\infty }a_nz^n $ in the unit disk $ \mathbb {D}=\{z\in \mathbb {C}:\lvert z\rvert <1\} $ is said to satisfy Bohr phenomenon if there exists an $ r_f>0 $ such that $$ \sum _{n=1}^{\infty }\lvert a_n\rvert r^n\leq d(f(0),\partial \mathbb {D}) $$ for every function $ f\in \mathcal {F} $, and $\lvert z\rvert =r\leq r_f $. The largest radius $ r_f $ is known as the Bohr radius and the inequality $ \sum _{n=1}^{\infty }\lvert a_n\rvert r^n\leq d(f(0),\partial f(\mathbb {D})) $ is known as the Bohr inequality for the class $ \mathcal {F} $, where $d$ is the Euclidean distance. In this paper, we prove several sharp improved and refined versions of Bohr-type inequalities in terms of area measure of functions in a certain subclass of analytic and univalent (i.e. one-to-one) functions. As a consequence, we obtain several interesting corollaries on the Bohr-type inequality for the class which are the harmonic analogue of some Bohr-type inequality for the class of analytic functions.

Sufficient conditions for univalence obtained by using the Ruscheweyh-Bernardi differential-integral operator

"In this paper we introduce the Ruscheweyh-Bernardi differential-integral operator $T^m:A\to A$ defined by $$T^m[f](z)=(1-\lambda )R^m [f](z)+\lambda B^m[f](z),\ z\in U,$$ where $R^m$ is the Ruscheweyh differential operator (Definition \ref{d1.2}) and $B^m$ is the Bernardi integral operator (Definition \ref{d1.1}). By using the operator $T^m$, the class of univalent functions denoted by $T^m(\lambda ,\beta )$, $0\le \lambda \le 1$, $0\le \beta <1$, is defined and several differential subordinations are studied."

A Certain Class of Analytic Functions Associated with Beta Negative Binomial Distribution Defined on Complex Hilbert Space

In this work , we show and research a new class of univalent and analytic functions with negative coefficients linked to the beta negative binomial distribution on a complicated Hilbert space. We find fascinating geometric features such as the convex set, coefficient estimates, distortion and growth theorems, starlikeness and convexity radii, and describe the extreme points for functions in this class.

Certain Subclasses of Univalent Functions Linked with q-Chebyshev Polynomial

The solutions provided in this work address the classic but still relevant topic of establishing new classes of univalent functions linked to $q$-Chebyshev polynomials and examining coefficient estimates features. Aspects of quantum calculus are also considered in this research to make it more unique and produce more pleasing outcomes. We introduce new classes of univalent functions connected to $q$-Chebyshev polynomials, which generalize certain previously investigated classes. The link among the previously published findings and the current ones are noted. For each of the new classes, estimates for the Taylor-Maclaurin coefficients $|r_2|$ and $|r_3|$ are derived and the much-studied Fekete-Szegö functional.

Results on a class of analytic functions with finitely many fixed coefficients related to a generalised multiplier transformation

A new class of univalent functions denoted by Tm(ξ,ϖ,σ,en) is defined and studied in this work. The class of functions Tm(ξ,ϖ,σ,en) generalises certain previously introduced classes of functions in the literature. Geometric properties of the class of functions in the class such as coefficient estimate, radius of starlikenes and radius convexity were studied.

Coefficient inequalities for classes of univalent functions defined by q derivatives

Using the principal of subordination and the qderivative, we obtain sharp bounds for some classes of univalent functions.

Sufficient conditions for univalence obtained by using Briot-Bouquet differential subordination

In this paper, we define the operator Im : differential-integral operator, where Sm is S˘al˘agean differential operator and Lm is Libera integral operator. By using the operator Im the class of univalent functions denoted by is defined and several differential subordinations are studied. Even if the use of linear operators and introduction of new classes of functions where subordinations are studied is a well-known process, the results are new and could be of interest for young researchers because of the new approach derived from mixing a differential operator and an integral one. By using this differential–integral operator, we have obtained new sufficient conditions for the functions from some classes to be univalent. For the newly introduced class of functions, we show that is it a class of convex functions and we prove some inclusion relations depending on the parameters of the class. Also, we show that this class has as subclass the class of functions with bounded rotation, a class studied earlier by many authors cited in the paper. Using the method of the subordination chains, some differential subordinations in their special Briot-Bouquet form are obtained regarding the differential–integral operator introduced in the paper. The best dominant of the Briot-Bouquet differential subordination is also given. As a consequence, sufficient conditions for univalence are stated in two criteria. An example is also illustrated, showing how the operator is used in obtaining Briot–Bouquet differential subordinations and the best dominant.

Hankel Determinants for Univalent Functions Related to the Exponential Function

Recently, two classes of univalent functions S e * and K e were introduced and studied. A function f is in S e * if it is analytic in the unit disk, f ( 0 ) = f ′ ( 0 ) − 1 = 0 and z f ′ ( z ) f ( z ) ≺ e z . On the other hand, g ∈ K e if and only if z g ′ ∈ S e * . Both classes are symmetric, or invariant, under rotations. In this paper, we solve a few problems connected with the coefficients of functions in these classes. We find, among other things, the estimates of Hankel determinants: H 2 , 1 , H 2 , 2 , H 3 , 1 . All these estimates improve the known results. Moreover, almost all new bounds are sharp. The main idea used in the paper is based on expressing the discussed functionals depending on the fixed second coefficient of a function in a given class.

Univalent Functions Formulated by the Salagean-Difference Operator

We present a class of univalent functions Tm(κ, α) formulated by a new differential-difference operator in the open unit disk. The operator is a generalization of the well known Salagean's differential operator. Based on this operator, we define a generalized class of bounded turning functions. Inequalities, extreme points of Tm(κ, α), some convolution properties of functions fitting to Tm(κ, α), and other properties are discussed.

Radius of Convexity of Sections of a Class of Close-to-Convex Functions of Order α

Abstract In this paper we study radius of convexity of sections of a class of univalent close-to-convex functions on 𝔻 = {z ∈ ℂ: |z| < 1}. For functions in this class, coefficient bounds, an integral representation and radius of convexity of nth sections have been obtained.

Best bound for λ- pseudo starlike functions

In this paper, we obtain sharp upper bound to the second Hankel determinant for the functions belong to the class of λ- pseudo starlike functions, an interesting sub class of univalent functions defined in the open unit disc E={z:|z|<1}, using Toeplitz determinants.

Applications of Livingston‐type inequalities to the generalized Zalcman functional

AbstractWe obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro–Warschawski class of univalent functions as well as for the closed convex hulls of the convex and starlike functions by using an inequality from [6]. In particular, we generalize an inequality proved by Ma for starlike functions and answer a question from his paper [17]. Finally, we prove an asymptotic version of the generalized Zalcman conjecture for univalent functions and discuss various related or equivalent statements which may shed further light on the problem.

On a class of univalent functions defined by Salagean integro-differential operator

On a class of univalent functions defined by Salagean integro-differential operator

Some properties for certain classes of univalent functions defined by differential inequalities

Let A be the space of functions analytic in the unit disk D={z: |z| < 1}. Let U denote the set of all functions f ɛ A satisfying the conditions f(0)=f′(0)−1=0 and |f′(z)(zf(z))2-1| <1(|z|<1). Also, let Ω denote the set of all functions f ɛ A satisfying the conditions f(0) = f′(0)-1 = 0 and |zf′(z)-f(z)| <12(|z|<1). In this article, we discuss the properties of U and Ω.

Rigidity and Parametric Embedding of Semi-complete Vector Fields on the Unit Disk

This manuscript contains recent results on generation theory of semigroups of holomorphic mappings with applications to geometric function theory as well as new results which could define some new trends in the development of the subject. We present various characterizations, properties and methods of parametric embedding of the class of semi-complete vector fields (holomorphic generators) and their relations to the classes of starlike and spirallike functions on the unit disk. In particular, we show that the class of univalent functions satisfying the Nashiro–Warshawskii condition consists of semi-complete vector fields. In a parallel manner, we present certain quantitative characteristics of boundary regular null points of semi-complete vector fields and corresponding backward flow invariant domains. In addition, we establish generalized infinitesimal versions of the Burns-Krantz rigidity theorem. Some open questions are discussed.

Some results of a class of univalent functions with negative coiffitions

In this paper, we study a new subclass of univalent analytic functions with positive coefficients in the unit disk; we obtain main result, distortion theorem and some properties of this subclass. Keywords : Univalent Functions, Distortion Theorem, Linear Combination.

Some Applications of a new class of Univalent Functions Defined by Subordination Property

In this paper, we introduce and study some applications of a new class of univalent functions defined by subordination property. Coefficient inequality, convex linear combinations, growth and distortion inequalities, radii of starlikeness, convexity and close-to- convexity and Hadamard product (or convolution) are given.