Differential Subordination Research Articles

Third-Order Differential Superordination Involving the Generalized Bessel Functions

There are many articles in the literature dealing with the first-order and the second-order differential subordination and differential superordination problems for analytic functions in the unit disk, but there are only a few articles dealing with the third-order differential subordination problems. The concept of third-order differential subordination in the unit disk was introduced by Antonino and Miller, and studied recently by Tang and Deniz. Let \(\Omega \) be a set in the complex plane \(\mathbb {C}\), let \(\mathfrak {p}(z)\) be analytic in the unit disk \(\mathbb {U}=\{z:z\in \mathbb {C}\quad \text {and} \quad |z|<1\}\), and let \(\psi : \mathbb {C}^4\times \mathbb {U}\rightarrow \mathbb {C}\). In this paper, we investigate the problem of determining properties of functions \(\mathfrak {p}(z)\) that satisfy the following third-order differential superordination: $$\begin{aligned} \Omega \subset \left\{ \psi (\mathfrak {p}(z),z\mathfrak {p}'(z),z^2\mathfrak {p}''(z), z^3\mathfrak {p}'''(z);z): z\in \mathbb {U}\right\} . \end{aligned}$$ As applications, we derive some third-order differential superordination results for analytic functions in \(\mathbb {U}\), which are associated with a family of generalized Bessel functions. The results are obtained by considering suitable classes of admissible functions. New third-order differential sandwich-type results are also obtained.

Differential Subordinations Involving Generalized Bessel Functions

In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some appropriate classes of admissible functions. We obtain also some sandwich-type results and we point out various known or new special cases of our main results.

Sandwich results for analytic functions involving with iterations of the Owa–Srivastava operator and its combination

In this paper, we investigate some strong differential subordination and strong differential superordination results for analytic functions, which involving the iterations of the Owa–Srivastava operator and its combination. Some new sandwich type results are also obtained.

On Differential Subordination, Superordination and Sandwich Theorems of Symmetric Analytic Functions

Abstract In this paper, we study the interesting properties of differential subor-dination and superordination for the classes of symmetric functions analytic in the unit disc. We derive sandwich results on the basis of this theory.

FIRST – ORDER STRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION PROPERTIES FOR ANALYTIC FUNCTIONS ASSOCIATED WITH LINEAR OPERATOR

In the present paper we study of some properties first - order strong differential subordination and superordination for analytic functions associated with Ruscheweyh derivative operator which are obtained by considering suitable classes of admissible functions.

Some applications of differential subordination to certain subclass of p-valent meromorphic functions involving convolution

Abstract By using the principle of differential subordination, we introduce subclass of p-valent meromorphic functions involving convolution and investigate various properties for this subclass. We also indicate relevant connections of the various results presented in this paper with those obtained in earlier works.

Fractional differential superordination

The notion of differential superordination was introduced by S.S. Miller and P.T. Mocanu as a dual concept of differential subordination. Recently, in Tamkang J. Math.[7], the author have introduced the notion of fractional differential subordination. In this work, we consider the dual problem of determining properties of analytic functions that satisfy the fractional differential superordination. By employing some types of admissible functions, involving differential operator of fractional order, we illustrate geometric properties such as starlikeness and convexity for a class of analytic functions in the unit disk. Moreover, applications are posed in the sequel.

Third-order differential subordination results for analytic functions involving the generalized Bessel functions

In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bκcf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z(Bκ+1cf(z))′ = κBκcf(z) - (κ - 1) Bκ+1cf(z)where b,c,p ℂ and κ = p + (b+1)/2 ∈ C\\(Z0- = {0, -1, -2,⋯}). The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.

Certain Admissible Classes of Multivalent Functions

We investigate some applications of the differential subordination and the differential superordination of certain admissible classes of multivalent functions in the open unit disk U. Several differential sandwich-type results are also obtained.

Differential Subordination with Generalized Derivative Operator of Analytic Functions

Motivated by generalized derivative operator defined by the authors (El-Yagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator Dλ1,λ2,δm,b are given.

A Note on Fractional Differential Subordination Based on the Srivastava-Owa Fractional Operator

In this work, we consider a definition for the concept of fractional differential subordination in sense of Srivastava-Owa fractional operators. By employing some types of admissible functions involving differential operator of fractional order, we illustrate applications.

Some Applications of Second-Order Differential Subordination on a Class of Analytic Functions Defined by Komatu Integral Operator

We introduce a new class of analytic functions by using Komatu integral operator and obtain some subordination results.

Some applications of differential subordination and the Dziok–Srivastava convolution operator

By making use of the principle of differential subordination and the Dziok–Srivastava convolution operator, we introduce and investigate three interesting subclasses of analytic and univalent functions in the open unit disk. We obtain their inclusion relationships and also show that these classes are closed under convolution with convex functions. The results presented in this paper provide generalizations of several recent works by (for example) Özkan and Altıntaş (2006) [16], Trojnar-Spelina (2008) [30], and many other authors.

Third Order Differential Subordination of Analytic Function Defined by Fractional Derivative Operator

Third Order Differential Subordination of Analytic Function Defined by Fractional Derivative Operator

Differential subordination and superordination results for certain subclasses of analytic functions by the technique of admissible functions

By investigating appropriate classes of admissible functions, various Differential subordination and superordination results for analytic functions in the open unit disk are obtained using Cho-Kwon-Srivastava operator. As a consequence of these results, Sandwich-type results are also obtained.

Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator

There are many articles in the literature dealing with the first-order and the second-order differential subordination and superordination problems for analytic functions in the unit disk, but only a few articles are dealing with the above problems in the third-order case (see, e.g., Antonino and Miller (2011) and Ponnusamy et al. (1992)). The concept of the third-order differential subordination in the unit disk was introduced by Antonino and Miller in (2011). Let Ω be a set in the complex planeC. Also letpbe analytic in the unit diskU=z:z∈C and z&lt;1and suppose thatψ:C4×U→C. In this paper, we investigate the problem of determining properties of functionsp(z)that satisfy the following third-order differential superordination:Ω⊂ψpz,zp′z,z2p′′z,z3p′′′z;z:z∈U. As applications, we derive some third-order differential subordination and superordination results for meromorphically multivalent functions, which are defined by a family of convolution operators involving the Liu-Srivastava operator. The results are obtained by considering suitable classes of admissible functions.

Differential Subordination Results for Analytic Functions in the Upper Half-Plane

There are many articles in the literature dealing with differential subordination problems for analytic functions in the unit disk, and only a few articles deal with the above problems in the upper half-plane. In this paper, we aim to derive several differential subordination results for analytic functions in the upper half-plane by investigating certain suitable classes of admissible functions. Some useful consequences of our main results are also pointed out.

Some Subordination Results onq-Analogue of Ruscheweyh Differential Operator

We derive theq-analogue of the well-known Ruscheweyh differential operator using the concept ofq-derivative. Here, we investigate several interesting properties of thisq-operator by making use of the method of differential subordination.

Some Properties of Certain Class of Analytic Functions

We obtain some properties related to the coefficient bounds for certain subclass of analytic functions. We also work on the differential subordination for a certain class of functions.

Applications of Differential Subordination for Argument Estimates of Multivalent Analytic Functions

By using the method of differential subordinations, we derive some properties of multivalent analytic functions. All results presented here are sharp.