Sufficient Conditions For Univalence Research Articles

A sufficient condition for univalence

A sufficient condition for univalence

Some sufficient conditions for univalence and close-to-convexity

Abstract In the class of analytic functions in the unit disc | z | < 1 {\lvert z\rvert<1} we prove some new sufficient conditions for functions to be univalent or to be close-to-convex in the unit disc. Also we extend Ozaki’s condition that ℜ ⁢ 𝔢 ⁢ { exp ⁡ ( i ⁢ α ) ⁢ f ( p ) ⁢ ( z ) } > 0 {\mathfrak{Re}\{\exp(i\alpha)f^{(p)}(z)\}>0} in | z | < 1 {\lvert z\rvert<1} implies that f ⁢ ( z ) {f(z)} is at most p-valent in | z | < 1 {\lvert z\rvert<1} .

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.

Some Simple Conditions for Univalence

Abstract We apply Ozaki–Umezawa's lemma on functions that are convex in one direction to find some sufficient conditions for univalence and closeness to convexity.

Some generalizations of the class of functions convex in one direction

This paper concerns the extension of univalent conditions known for a ring domain to the case of a half-plane. We study the possibilities of applying Rahman and Brickman methods to functions analytic in the upper half-plane. Some generalizations of the functions convex in one direction are obtained. We also investigate the curvelinear half-planes, the boundary of which can be attained by a family of shift curves, and demonstrate the efficiency of the quasiconformal extension method. The subclasses of domains, whose boundaries are quasiconformal curves, are identified. Some sufficient conditions for univalence of functions analytic in these domains are established.

Sufficient conditions for univalence - Univalence of Certain Integral Operators Involving Generalized Struve functions

Sufficient conditions for univalence - Univalence of Certain Integral Operators Involving Generalized Struve functions

Univalence results for slice regular functions of a quaternion variable

The goal of this paper is study the univalence property of slice regular functions of quaternion variable. We prove a number of results, among which several sufficient conditions for univalence, an area-type Theorem, and a Bieberbach–de Branges Theorem for a subclass of slice regular functions. We also discuss some geometric and algebraic interpretations of our results in terms of maps from to itself.

An extension of a basic univalence criterion

Some sufficient conditions for univalence and quasiconformal extension of a class of functions defined by an integral operator are discussed with some examples. This condition involves two arbitrary functions $ g $ and $ h $ analytic in the unit disk. A number of well-known univalent conditions would follow upon specializing the functions and the parameters involved in our main result.

Univalence criteria for meromorphic functions and quasiconformal extensions

The aim of this paper is to obtain sufficient conditions for univalence of meromorphic functions in the . Also, we refine a quasiconformal extension criterion with the help of Becker’s method. A number of univalence conditions would follow upon specializing the parameters involved in our main results. MSC:30C80, 30C45, 30C62.

Ahlfors's quasiconformal extension condition and $\Phi$-likeness

The notion of Φ-like functions is known to be a necessary and sufficient condition for univalence. By applying the idea, we derive several necessary conditions and sufficient conditions for that an analytic function defined on the unit disk is not only univalent but also has a quasiconformal extension to the Riemann sphere, as generalizations of well-known univalence and quasiconformal extension criteria, in particular, Ahlfors’s quasiconformal extension condition.

On some sufficient conditions for univalence and starlikeness

In this work, the conditions for univalence, starlikeness and convexity are discussed. MSC:30C45, 30C80.

Univalence criterion and quasiconformal extension of holomorphic mappings

In this paper we are concerned with solutions, in particular with the univalent solutions, of the Loewner differential equation associated with non-normalized subordination chains on the Euclidean unit ball B in \({\mathbb{C}^n}\). We also give applications to univalence conditions and quasiconformal extensions to \({\mathbb{C}^n}\) of holomorphic mappings on B. Finally we consider the asymptotical case of these results. The results in this paper are complete generalizations to higher dimensions of well known results due to Becker. They improve and extend previous sufficient conditions for univalence and quasiconformal extension to \({\mathbb{C}^n}\) of holomorphic mappings on B.

The univalence of general integral operator Bazilevič

Abstract In this paper we define a general integral operator Bazilevič and we obtain sufficient conditions for univalence of this integral operator.

Construction of sufficient conditions for univalence in a curvilinear sector

We study the domains representing a curvilinear sector. The subclasses of domains whose boundaries are quasiconformal curves are determined. Some sufficient univalence conditions for functions analytic in these domains are constructed.

On a Univalent Class Involving Differential Subordinations with Applications

Problem statement: By means of the Hadamard product (or convolution), new class of analytic functions was formed. This class was motivated by many authors. Approach: By using the concept of the subordination and superordination, we define certain differential inequalities and first order differential subordinations. Results: As their applications, we obtain some sufficient conditions for univalence which generalize and refine some previous results. Sandwich theorem is also obtained. Conclusion: Therefore, we posed a new class of analytic functions which generalized some well known subclasses. This class involves the E(Φ,ψ) - family of functions.

Sufficient conditions for univalence obtained by using second order linear strong differential subordinations

The concept of differential subordination was introduced in [3] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2] by J.A. Antonino and S. Romaguera. In [5] we have studied the strong differential subordinations in the general case and in [6] we have studied the first order linear strong differential subordinations. In this paper we study the second order linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively.

A Condition for Univalence in the Polydisk

We study a sufficient condition for univalence in the polydisk in terms of the size of the norm of the Schwarzian operator. Examples show that our result is close to optimal in dimension two. This paper extends work by the second author concerning similar criteria in the ball.

On a bounded subclass of certain analytic functions satisfying a differential inequality

In the present paper, using Jack's lemma, the authors investigate the differential in- equality (1 − α) Ip(n,λ)f(z) zp + α Ip(n+1,λ)f(z) Ip(n,λ)f (z) − 1 < μ, z ∈ E regarding multivalent functions defined by multiplier transfomation in the open unit disk E = {z : |z| < 1}. As consequences, sufficient conditions for univalence, starlikeness and strongly starlikeness of certain analytic functions are obtained.

Sufficient Conditions for Univalence of an Integral Operator

In this paper we have introduced an integral general operator. For this general operator which is a generalization of more known integral operators we have demonstrated some univalence properties.

Some sufficient conditions for univalence and close-to-convexity

The author uses the method of differential subordinations to obtain some new criteria for a normalised regular function, in unit disc $E=\{z: |z|