New Class Of Analytic Functions Research Articles

Two New Classes of Analytic Functions Defined by Strong Differential Subordinations and Superordinations

Abstract In the present investigation, by making use of strong differential subordinations and superordinations, we introduce and study two new classes of holomorphic functions containing generalized differential operator. Also we determine important properties for functions belongs to these classes.

On a class of analytic functions associated to a complex domain concerning q-differential-difference operator

In our current investigation, we apply the idea of quantum calculus and the convolution product to amend a generalized Salagean q-differential operator. By considering the new operator and the typical version of the Janowski function, we designate definite new classes of analytic functions in the open unit disk. Significant properties of these modules are considered, and recurrent sharp consequences and geometric illustrations are realized. Applications are considered to find the existence of solutions of a new class of q-Briot–Bouquet differential equations.

Class of Analytic Functions Defined by q-Integral Operator in a Symmetric Region

The aim of the present paper is to introduce a new class of analytic functions by using a q-integral operator in the conic region. It is worth mentioning that these regions are symmetric along the real axis. We find the coefficient estimates, the Fekete–Szegö inequality, the sufficiency criteria, the distortion result, and the Hankel determinant problem for functions in this class. Furthermore, we study the inverse coefficient estimates for functions in this class.

The Application of Generalized Quasi-Hadamard Products of Certain Subclasses of Analytic Functions with Negative and Missing Coefficients

In this paper, we introduce a new generalized differential operator using a new generalized quasi-Hadamard product, and certain new classes of analytic functions using subordination. We obtain certain results concerning the closure properties of the generalized quasi-Hadamard products and the generalized differential operators for this new subclasses of analytic functions with negative and missing coefficients.

New Symmetric Differential and Integral Operators Defined in the Complex Domain

The symmetric differential operator is a generalization operating of the well-known ordinary derivative. These operators have advantages in boundary value problems, statistical studies and spectral theory. In this effort, we introduce a new symmetric differential operator (SDO) and its integral in the open unit disk. This operator is a generalization of the Sàlàgean differential operator. Our study is based on geometric function theory and its applications in the open unit disk. We formulate new classes of analytic functions using SDO depending on the symmetry properties. Moreover, we define a linear combination operator containing SDO and the Ruscheweyh derivative. We illustrate some inclusion properties and other inequalities involving SDO and its integral.

A certain properties of a class of analytic functions defined by a generalized Srivastava-Attiya operator

In this article, we introduce a new class of analytic functions defined by generalized Srivastava-Attiya operator. Coefficient inequalities, convex combinations are obtained.

A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator

In our present investigation, we use the technique of convolution and quantum calculus to study the Salagean q-differential operator. By using this operator and the concept of the Janowski function, we define certain new classes of analytic functions. Some properties of these classes are discussed, and numerous sharp results such as coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, and integral mean inequalities of functions belonging to these classes are obtained and studied.

On Fekete-Szego Problem Associated with q-derivative Operator

In this paper, we define a new derivative operator associated with quantum calculus. Motivated by this new operator, we introduce two new classes of analytic functions and obtain the Fekete-Szego inequality.

On a new class of analytic functions with respect to symmetric points involving the q-derivative operator

In this paper we introduce a new subclass of analytic functions with respect to symmetric points involving the q-derivative operator. We find coefficient bounds and Fekete-Szego inequalities for functions belonging to these class. Relevant connections with previous results are pointed out.

Some Subclasses of a New Class of Analytic Functions under Fekete-Szegö Inequality

Some Subclasses of a New Class of Analytic Functions under Fekete-Szegö Inequality

A New Class of Analytic Functions Associated with Sălăgean Operator

The main object of the present paper is to investigate a number of useful properties such as inclusion relation, distortion bounds, coefficient estimates, and subordination results for a new subclass of analytic functions which are defined here by means of a linear operator. Several known consequences of the results are also pointed out.

Second-Order Differential Subordinations on a Class of Analytic Functions Defined by the Rafid Operator

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

Gleason’s Problem Associated to a Real Ternary Algebra and Applications

This paper is an introduction of a new class of analytic functions defined on a ternary algebra, a three dimensional structure different from $${{\mathbb {C}}}\times {{\mathbb {R}}}$$ , i.e. a real commutative algebra given by the linear span of $$\{1,\mathbf{e},\mathbf{e}^2\}$$ , where $$\mathbf{e}\not \in {{\mathbb {C}}}$$ is a generating unit. We define a single ternary conjugate and we build a new analytic function theory, different from previous approaches, on the basis of this single conjugation (akin to the quaternionic case). We give the solution to the Gleason problem which gives rise to Fueter-type variables and study the space of rational functions in this case.

On a Subclass of Starlike Functions

In this article, we define a new class of analytic functions. This class generalizes the class of $$k-\mathcal {UCV}$$ . We obtain some relationships of this class with other subclasses of analytic functions. Further we obtain the order of strongly starlikeness of this class of functions.

On a Generalization of Bounded Univalent Function of Complex Order

In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized differential operator Dnλ, μ.

SOME PROPERTIES FOR CERTAIN ANALYTIC FUNCTIONS

In this paper,we define a new class of analytic functions C(λ,β,A,B),which is the generalization of the class of analytic functions of the paper of Xang Ding-gong.The object of the present paper is to derive distortion theorems,real-part estimates,coefficient estimates etc.for the class C(λ,β,A,B).

New Subclass of Analytic Functions in Conical Domain Associated with Ruscheweyh q-Differential Operator

In this paper, we consider a new class of analytic functions which is defined by means of a Ruscheweyh q-differential operator. We investigated some new results such as coefficients inequalities and other interesting properties of this class. Comparison of new results with those that were obtained in earlier investigation are given as Corollaries.

Analytic Functions Related with Mocanu Class

In this article, we define a new class of analytic functions. This class generalizes the mocanu class. We obtain relationships of this class with other subclasses of analytic functions and derived many interesting results.

ON NEW CLASSES OF ANALYTIC FUNCTIONS IMPOSED VIA THE FRACTIONAL ENTROPY INTEGRAL OPERATOR

In this paper, we aim to introduce some geometric properties of analytic functions by utilizing the concept of fractional entropy in a complex domain. We extend the fractional entropy, type Tsallis entropy in the complex z-plane, by using some analytic functions. Established by this diffusion,we state specic new classes of analytic functions (type Schwarz function). Other geometric properties are validated in the sequel. Our development is completed by the Euler form Lemma and Jack Lemma.

On a class of analytic functions related to conic domains involving q-calculus

The theory of q-analysis has many applications in various subfields of mathematics and quantum physics. Research work in connection with function theory and q-theory together was first introduced by Ismail et al. [6]. Till now only non-significant interest in this area was shown although it deserves more attention. Exploiting this, we aim to introduce a new class of analytic functions that are closely related to the domains bounded by conic sections. The authors hope this article will motivate future researchers to work in the area of q-calculus which can find many applications in the theory of hypergeometric series and quantum theory.