Subordination Properties Research Articles

Results on Third-Order Differential Subordination for Analytic Functions Related to a New Integral Operator

In this paper, we aim to give some results for third-order differential subordination for analytic functions in the open unit disk U=z:z∈C and z<1 involving the new integral operator μα,nm(f∗g). The results are obtained by examining pertinent classes of acceptable functions. New findings on differential subordination have been obtained. Additionally, some specific cases are documented. This work investigates appropriate classes of admissible functions, presents a novel of new integral operator, and discusses the properties of third-order differential subordination. The properties and results of the differential subordination are symmetrical to the properties of the differential superordination to form the sandwich theorems.

Some Properties for Certain Subclasses of Spiral-Like and Robertson Analytic Functions

Making use of the definition of subordination, we introduce certain subclasses of spiral-like and Robertson functions in the open unit disk and study some important results such as convolution results, coefficients estimate, subordination properties and Fekete-Szego problems for these subclasses. Further, some known and new outcomes which follow as special cases of our outcomes are also mentioned.

محدد هنكل الثاني لفئة معينة من الدوال المعرفة بواسطة مؤثر تفاضلي

The objective of this paper is to obtain an upper bound of second Hankel determinant for a class of functions M_(α,β,λ,δ)^k (φ) defined in the open unit disc U by using the differential operator〖 D〗_(α,β,λ,δ)^k f(z). In addition, we give particular values to the parameters A,B and k to study special cases of the results of this article. The class M_(α,β,λ,δ)^k (φ) and the differential operator〖 D〗_(α,β,λ,δ)^k f(z). Key words: differential operator, Second Hankel determinant, Starlike functions, Subordination property

Subordination properties and coefficient problems for a novel class of convex functions

Abstract In this study, a novel family of analytical functions connected to convex functions in the open unit is introduced and investigated. Additionally, relationships between this class and other subclasses of analytic functions are deduced. Further, different results for the mentioned class and several new interesting properties are obtained.

On Certain Analogues of Noor Integral Operators Associated with Fractional Integrals

In this paper, we employ a q-Noor integral operator to perform a q-analogue of certain fractional integral operator defined on an open unit disc. Then, we make use of the Hadamard convolution product to discuss several related results. Also, we derive a class of convex functions by utilizing the q-fractional integral operator and apply the inspired presented theory of the differential subordination, to geometrically explore the most popular differential subordination properties of the aforementioned operator. In addition, we discuss an exciting inclusion for the given convex class of functions. Over and above, we investigate the q-fractional integral operator and obtain some applications for the differential subordination.

Briot–Bouquet Subordination Properties for Analytic Functions Involving Choi–Saigo–Srivastava Integral Operator

We consider a new subclass of starlike functions involving the Choi–Saigo–Srivastava integral operator associated with the sine function in open unit disc. In view of this function class, we examine majorization properties and Briot–Bouquet differential subordination relations for such functions.

On a characterization of starlike functions with respect to (2ȷ,ℓ)-symmetric conjugate points

In this paper, we introduce and study a new subclass of starlike functions with respect to [Formula: see text]-symmetric conjugate points using the principle of subordination. Several relationship with the well-known classes have been established. We have focussed on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of the results are presented here as corollaries, most of which are extensions of well-known results.

Determination of some properties of starlike and close-to-convex functions according to subordinate conditions with convexity of a certain analytic function

UDC 517.5 Investigation of the theory of complex functions is one of the most fascinating aspects of theory of complex analytic functions of one variable. It has a huge impact on all areas of mathematics. Many mathematical concepts are explained when viewed through the theory of complex functions. Let f ( z ) ∈ A , f ( z ) = z + ∑ n ≥ 2 ∞ a n z n , be an analytic function in the open unit disc normalized by f ( 0 ) = 0 and f ' ( 0 ) = 1. For close-to-convex and starlike functions, new and different conditions are obtained by using subordination properties, where r is a positive integer of order 2 - r ( 0 < 2 - r ≤ 1 2 ) . By using subordination, we propose a criterion for f ( z ) ∈ S * [ a r , b r ] . The relations for starlike and close-to-convex functions are investigated under certain conditions according to their subordination properties. At the same time, we analyze the convexity of some analytic functions and study their regional transformations. In addition, the properties of convexity for f ( z ) ∈ A are examined.

Sandwich-Type Theorems for a Family of Non-Bazilevič Functions Involving a q-Analog Integral Operator

This article presents a new q-analog integral operator, which generalizes the q-Srivastava–Attiya operator. Using this q-analog operator, we define a family of analytic non-Bazilevič functions, denoted as Tq,τ+1,uμ(ϑ,λ,M,N). Furthermore, we investigate the differential subordination properties of univalent functions using q-calculus, which includes the best dominance, best subordination, and sandwich-type properties. Our results are proven using specialized techniques in differential subordination theory.

Properties of Differential Subordination and Superordination for Multivalent Functions Associated with the Convolution Operators

Using convolution (or Hadamard product), we define the El-Ashwah and Drbuk linear operator, which is a multivalent function in the unit disk U=w:w<1 and w∈₵, and satisfy its specific relationship to derive the subordination, superordination, and sandwich results for this operator by using properties of subordination and superordination concepts.

Generalized $ q $-convex functions characterized by $ q $-calculus

<abstract><p>The objective of the current examination is to present new sub-classes of $ q $-convex and $ q $-starlike functions inside $ \mathcal E = \left\{z\in\mathbb C: \left|z\right| < 1\right\} $, by $ q $-difference operator. We determined connections of these classes and acquired a few fundamental properties, for instance, inclusion relation, subordination properties and $ q $-limits on real part.</p></abstract>

Fuzzy differential for subclass of analytic functions defined by linear operator

In this work, we establish some results for fuzzy differential for analytic functions associated with the Hadamard product for generalization Srivastava-Attiya operator is defined in the open unit disc L = {w ∈ C: |w| < 1}. In the present paper, the operator is applied to a new class of analytic functions with the Hadamard product. The goal of this article is to study some properties of fuzzy differential subordination and fuzzy differential superordination of analytic functions related to the Hadamard product. Using double theories, a sandwich-type theorem was obtained.

Subordination Properties of Certain Operators Concerning Fractional Integral and Libera Integral Operator

The results contained in this paper are the result of a study regarding fractional calculus combined with the classical theory of differential subordination established for analytic complex valued functions. A new operator is introduced by applying the Libera integral operator and fractional integral of order λ for analytic functions. Many subordination properties are obtained for this newly defined operator by using famous lemmas proved by important scientists concerned with geometric function theory, such as Eenigenburg, Hallenbeck, Miller, Mocanu, Nunokawa, Reade, Ruscheweyh and Suffridge. Results regarding strong starlikeness and convexity of order α are also discussed, and an example shows how the outcome of the research can be applied.

Revised Manuscript On New Sandwich Results of Univalent Functions Defined by a Linear Operator

In this research paper, we explain the use of the convexity and the starlikness properties of a given function to generate special properties of differential subordination and superordination functions in the classes of analytic functions that have the form in the unit disk. We also show the significant of these properties to derive sandwich results when the Srivastava- Attiya operator is used.

On Classes of Non-Carathéodory Functions Associated with a Family of Functions Starlike in the Direction of the Real Axis

In this paper, we introduce a new class of analytic functions subordinated by functions which is not Carathéodory. We have obtained some interesting subordination properties, inclusion and integral representation of the defined function class. Several corollaries are presented to highlight the applications of our main results.

A Differential Operator Associated with q-Raina Function

The topics studied in the geometric function theory of one variable functions are connected with the concept of Symmetry because for some special cases the analytic functions map the open unit disk onto a symmetric domain. Thus, if all the coefficients of the Taylor expansion at the origin are real numbers, then the image of the open unit disk is a symmetric domain with respect to the real axis. In this paper, we formulate the q-differential operator associated with the q-Raina function using quantum calculus, that is the so-called Jacksons’ calculus. We establish a new subclass of analytic functions in the unit disk by using this newly developed operator. The theory of differential subordination inspired our approach; therefore, we geometrically explore the most popular properties of this new operator: subordination properties, coefficient bounds, and the Fekete-Szegő problem. As special cases, we highlight certain well-known corollaries of our primary findings.

Certain subclasses of meromorphic multivalent q-starlike and q-convex functions

Abstract In this paper, we extend the idea of q-derivative (or q-difference) operator for meromorphic p-valent functions and introduce certain new subclasses of meromorphic multivalent q-starlike and q-convex functions. We investigate subordination properties, coefficient inequalities, convolution properties and integral representations. We also derive sufficient conditions for meromorphic multivalent q-starlike and q-convex functions and highlight some known consequence of our main results.

Bazilevič Functions of Complex Order with Respect to Symmetric Points

In this paper, we familiarize a class of multivalent functions with respect to symmetric points related to the differential operator and discuss the impact of Janowski functions on conic regions. Inclusion results, the subordination property, and coefficient inequalities are obtained. Further, the applications of our results that are extensions of those given in earlier works are presented as corollaries.

Subordination Involving Regular Coulomb Wave Functions

The functions 1+z, ez, 1+Az, A∈(0,1] map the unit disc D to a domain which is symmetric about the x-axis. The Regular Coulomb wave function (RCWF) FL,η is a function involving two parameters L and η, and FL,η is symmetric about these. In this article, we derive conditions on the parameter L and η for which the normalized form fL of FL,η are subordinated by 1+z. We also consider the subordination by ez and 1+Az, A∈(0,1]. A few more subordination properties involving RCWF are discussed, which leads to the star-likeness of normalized Regular Coulomb wave functions.

On some differential subordination theorems of multivalent functions involving integral operator

This paper is concerned with the differential subordination properties of the multivalent functions involving by generalized integral operator. We investigate some applications of a differential subordination results for a normalized multivalent analytic function ( ( ) ) and is a generalized integral operator on the class of all analytic functions. Some of our results generalized previously known results. Keywords — Analytic functions; p–valent; integral operator; differential subordination.