Dziok-Srivastava Operator Research Articles

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.

Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator

Fuzzy set theory, introduced by Zadeh, gives an adaptable and logical solution to the provocation of introducing, evaluating, and opposing numerous sustainability scenarios. The results described in this article use the fuzzy set concept embedded into the theories of differential subordination and superordination from the geometric function theory. In 2011, fuzzy differential subordination was defined as an extension of the classical notion of differential subordination, and in 2017, the dual concept of fuzzy differential superordination appeared. These dual notions are applied in this paper regarding the fractional integral applied to Dziok–Srivastava operator. New fuzzy differential subordinations are proved using known lemmas, and the fuzzy best dominants are established for the obtained fuzzy differential subordinations. Dual results regarding fuzzy differential superordinations are proved for which the fuzzy best subordinates are shown. These are the first results that link the fractional integral applied to Dziok–Srivastava operator to fuzzy theory.

On Harmonic Univalent Functions Defined by Dziok-Srivastava Operator

The purpose of this work is to present a class of harmonic univalent functions defined by the Dziok-Srivastava operator. Some geometric properties like coefficients conditions, distortion theorem, convolution (Hadamard product), convex combination and extreme points are investigated.
 2000 Mathematics Subject Classification: 30C45, 30C50

Some Properties of Mesomorphic Univalent Functions with Negative Coefficients Defined

The main aim of the present investigation is to introduce a new class of meromorphic univalent functions with negative coefficients defined by Dziok-Srivastava operator. Some geometric properties are introduced, like coefficient estimate, integral operator, Feket-Szegӧ bounds for this class of meromorphic functions.

Subordination and superordination results of multivalent functions associated with the Dziok-Srivastava operator

Using the techniques of the differential subordination and superordination, we derive certain subordination and superordination properties of multivalent functions associated with the Dziok-Srivastava operator.

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.

Some properties of p-valent analytic functions defined by Dziok–Srivastava operator

Using the Dziok–Srivastava operator, we describe the class of p-valent analytical functions [Formula: see text] and we obtain certain interesting properties of this class.

Other Subordination Results for Fractional Integral Associated with Dziok Srivastava Operator

In this paper we have discussed differential subordination properties associated with the fractional integral by using Dziok-Srivastava operator

Harmonic Function with Correlated Coefficients

In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

Pre-Schwarzian norm for linear operators of uniformly convex functions of order α and type β

Abstract By making use of the pre-Schwarzian norm given by we obtain such norm estimates for Hohlov operator of functions belonging to the class of uniformly convex functions of order α and type β. We also employ an entirely new method to generalize and extend the results of Theorems 1, 2 and 3 in [3]. Finally, some inequalities concerning the norm of the pre-Schwarzian derivative for Dziok-Srivastava operator are also considered.

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.

Differential Subordinations for Higher-Order Derivatives of Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

Differential Subordinations for Higher-Order Derivatives of Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

The Fekete–Szegö problem for a Ma–Minda type class of bi-univalent functions associated with the Hohlov operator

In this paper, we solve Fekete–Szegö problem for a Ma–Minda type class [Formula: see text] of bi-univalent functions associated with the Hohlov operator which is a specialized case of the widely-investigated Dziok–Srivastava operator which, in turn, is contained in the Srivastava–Wright operator. Results for some of its consequent classes [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] are also given. A function [Formula: see text] in this class may satisfy one subordinate condition, whereas [Formula: see text], another. One result for that is also given by considering certain [Formula: see text]. Some useful consequences and relationships with some of the known results are also pointed out.

Some subclasses of meromorphically multivalent functions associated with the Dziok-Srivastava operator

We introduce two new subclasses Hp,k(?,A,B) and Qp,k(?,A,B) of meromorphically multivalent functions associated with the Dziok-Srivastava operator which is a special case of the Srivastava-Wright operator. Distortion inequalities, partial sums and convolutional theorems for Hp,k(?,A,B) and Qp,k(?,A,B) are obtained.

On some analytic functions associated with the linear operators satisfying certain recurring relations

In this paper, associated with convolutions, linear operators [Formula: see text] and [Formula: see text] are defined with the requirement of certain recurring relations. Some results based on analytic functions involving these operators are derived. Taking some specific forms of such operators, results involving the Dziok–Srivastava operator, the Jung–Kim–Srivastava integral operator, the Srivastava–Attiya linear operator and others, are also mentioned.

On a subclass of Goodman-Ronning type harmonic univalent functions defined by Dziok-Srivastava operator

The aim of this paper is to investigate a subclass of Goodman-Ronning type of harmonic univalent functions defined by the modified Dziok-Srivastava operator. The properties for this class such as the coefficient conditions, distortions bounds and extreme points are investigated.

Holder's Inequalities for a New Class of P-Valent Analytic Functions

In this paper, we introduced a new class of p-valent analytic functions using a linear multiplier Dziok-Srivastava operator D m;q;s f(z)(m2 N0 =f0; 1;:::g;

Certain subclasses of analytic functions of complex order involving the generalized Dziok-Srivastava operator

Certain subclasses of analytic functions of complex order involving the generalized Dziok-Srivastava operator

Majorization for Certain Classes of Analytic Functions Defined by the Inverse of the Dziok-Srivastava Operator

In the present paper, the author investigates the majorization problems for certain subclasses of p-valently analytic functions in the open unit disk U dened by the inverse of the Dziok-Srivastava operator. Relevant connections of the results presented in this paper with those given by earlier authors are also pointed out.

Fekete–Szegö problem for certain classes of analytic functions of complex order defined by the Dziok–Srivastava operator

By using the hypergeometric function defined by the Dziok–Srivastava operator, new subclasses of analytic functions are introduced. For these classes, the Fekete–Szego problem is obtained. Various known or new special cases of our results are pointed out.