Strong Differential Subordination Research Articles

Theorems of Strong Differential Sandwich Results for Analytic Functions Associated with Wanas Fractional Integral Operator

The objective of this research is to produce robust differential subordination and differential superordination results using the fractional integral of the Wanas differential operator. These results apply to Analytic functions defined on , with Coefficient functions that are holomorphic in Furthermore, for each instance of strong differential subordination and strong differential superordination, we provide the most superior dominant and the most subordinate subordinant. These findings are used to achieve strong sandwich results.

Strong Differential Subordinations and Superordinations for Riemann–Liouville Fractional Integral of Extended q-Hypergeometric Function

The notions of strong differential subordination and its dual, strong differential superordination, have been introduced as extensions of the classical differential subordination and superordination concepts, respectively. The dual theories have developed nicely, and important results have been obtained involving different types of operators and certain hypergeometric functions. In this paper, quantum calculus and fractional calculus aspects are added to the study. The well-known q-hypergeometric function is given a form extended to fit the study concerning previously introduced classes of functions specific to strong differential subordination and superordination theories. Riemann–Liouville fractional integral of extended q-hypergeometric function is defined here, and it is involved in the investigation of strong differential subordinations and superordinations. The best dominants and the best subordinants are provided in the theorems that are proved for the strong differential subordinations and superordinations, respectively. For particular functions considered due to their remarkable geometric properties as best dominant or best subordinant, interesting corollaries are stated. The study is concluded by connecting the results obtained using the dual theories through sandwich-type theorems and corollaries.

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

In 2012, new classes of analytic functions on U×U¯ with coefficient holomorphic functions in U¯ were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok–Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok–Srivastava operator, we obtain a new operator Dz−γHmlα1,β1 that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok–Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential subordinations and superordinations concerning the operator Dz−γHmlα1,β1 are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties.

Strong Differential Subordination and Superordination Results for Extended q-Analogue of Multiplier Transformation

The results obtained by the authors in the present article refer to quantum calculus applications regarding the theories of strong differential subordination and superordination. The q-analogue of the multiplier transformation is extended, in order to be applied on the specific classes of functions involved in strong differential subordination and superordination theories. Using this extended q-analogue of the multiplier transformation, a new class of analytic normalized functions is introduced and investigated. The convexity of the set of functions belonging to this class is proven and the symmetry properties derive from this characteristic of the class. Additionally, due to the convexity of the functions contained in this class, interesting strong differential subordination results are proven using the extended q-analogue of the multiplier transformation. Furthermore, strong differential superordination theory is applied to the extended q-analogue of the multiplier transformation for obtaining strong differential superordinations for which the best subordinants are provided.

Differential Sandwich Theorems for Atangana–Baleanu Fractional Integral Applied to Extended Multiplier Transformation

In this paper we derive subordination and superordination results regarding the Atangana–Baleanu fractional integral applied to multiplier transformation and we give several differential sandwich-type theorems. Then, we apply the Atangana–Baleanu fractional integral to extended multiplier transformation on the class A ζ ∗ of normalized analytic functions and we derive strong differential subordination and strong differential superordination results regarding the extended new operator and we give the corresponding differential sandwich-type theorems from the first part of the paper.

Applications of Confluent Hypergeometric Function in Strong Superordination Theory

In the research presented in this paper, confluent hypergeometric function is embedded in the theory of strong differential superordinations. In order to proceed with the study, the form of the confluent hypergeometric function is adapted taking into consideration certain classes of analytic functions depending on an extra parameter previously introduced related to the theory of strong differential subordination and superordination. Operators previously defined using confluent hypergeometric function, namely Kummer–Bernardi and Kummer–Libera integral operators, are also adapted to those classes and strong differential superordinations are obtained for which they are the best subordinants. Similar results are obtained regarding the derivatives of the operators. The examples presented at the end of the study are proof of the applicability of the original results.

Strong Differential Sandwich Results for Bazilevic-Sakaguchi Type Functions Associated with Admissible Functions

In the present article, we define a new family for holomorphic functions (so-called Bazilevic-Sakaguchi type functions) and determinate strong differential subordination and superordination results for these new functions by investigating certain suitable classes of admissible functions. These results are applied to obtain strong differential sandwich results.

Strong subordination and superordination with sandwich-type theorems using integral operators

The notions of strong differential subordination and superordination have been studied recently by many authors. In the present paper, using these concepts, we obtain some preserving properties of certain nonlinear integral operator defined on the space of normalized analytic functions in $\mathbb{D}\times\overline{\mathbb{D}}$. The sandwich-type theorems and consequences of the main results are also considered.

Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯),f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

Strong Subordination for P-Valent Functions Involving A Linear Operator

The concept of strong differential subordination was introduces in [1], [2] by Antonio and Romaguera and developed in [4]. The object of the present paper is to investigate some inclusion relations and other interesting properties for p-valent functions defined in the open unit disk of the complex plane involving linear operator by using the principle of strong differential subordination

Some New Results of Differential Subordinations for HigherOrder Derivatives of Multivalent Functions

The main purpose of this paper is to study the differential subordination result for multivalent analytic functions. We give some applications of higher-order differential subordination results involving Hadamard product for multivalent analytic functions with generalized hypergeometric function in open unit disk. We have also discussed and studied a new class of higher-order derivatives of multivalent analytic functions in open unit disk of complex plane related to linear operator and we obtain some results connected inclusion relationship, argument estimate, integral representation and subordination property. by using the method of differential subordination we aim to prove some classical results in multivalent functions theory. We obtain some interesting properties of this class and establish several strong differential subordination for higher-order derivatives of multivalent analytic functions. By making use of the principle of subordination, we introduce a new class W_(p, q)^(l, k) (η,α_1, m; h) for higher-order derivatives of multivalent analytic functions associated with Dziok-Srivastava operator. We obtain some result for this class.

Strong Subordination for E -valent Functions Involving the Operator Generalized Srivastava-Attiya

Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

Some Properties for Strong Differential Subordination of Analytic Functions Involving Ruscheweyh Derivative Operator

In this paper, we introduce and study some properties for strong differential subordinations of analytic functions associated with Ruscheweyh derivative operator defined in the open unit disk and closed unit disk of the complex plane.

Some Properties for Strong Differential Subordination of Analytic Functions Associated with Wanas Operator

In this paper, by making use of Wanas operator, we derive some properties related to the strong differential subordinations of analytic functions defined in the open unit disk and closed unit disk of the complex plane.

New Strong Differential Subordination and Superordination of Meromorphic Multivalent Quasi-Convex Functions

New Strong Differential Subordination and Superordination of Meromorphic Multivalent Quasi-Convex Functions

Strong differential subordinates for noncommutative submartingales

We introduce a notion of strong differential subordination of noncommutative semimartingales, extending Burkholder’s definition from the classical case (Ann. Probab. 22 (1994) 995–1025). Then we establish the maximal weak-type $(1,1)$ inequality under the additional assumption that the dominating process is a submartingale. The proof rests on a significant extension of the maximal weak-type estimate of Cuculescu and a Gundy-type decomposition of an arbitrary noncommutative submartingale. We also show the corresponding strong-type $(p,p)$ estimate for $1<p<\infty $ under the assumption that the dominating process is a nonnegative submartingale. This is accomplished by combining several techniques, including interpolation-flavor method, Doob–Meyer decomposition and noncommutative analogue of good-$\lambda$ inequalities.

Strong Differential Subordination Results for Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

In this paper, by making use of the principle of strong subordination, we establish some interesting properties of multivalent analytic functions defined in the open unit disk and closed unit disk of the complex plane associated with Dziok-Srivastava operator.

Strong differential subordination and superordination of analytic functions in connection with a linear operator

Strong differential subordination and superordination of analytic functions in connection with a linear operator

Some results for strong differential subordination of analytic functions defined by differential operator

The purpose of this paper is to introduce some results associated with the strong differential subordinations of analytic functions defined in the open unit disk and closed unit disk of the complex plane.

Admissible classes of analytic functions associated with generalized Struve functions

In the present paper, by considering suitable classes of ad- missible functions we investigate some strong differential subordination as well as superordination results for analytic functions associated with normalized form of the generalized Struve functions. As a consequence of these results, new strong differential Sandwich-type results are ob- tained.