Carlson-Shaffer Operator Research Articles

Certain New Subclassess of Analytic function using Carlson- Shaffer operator

By making use of Carlson-Shaffer operator and P [ X, Y], we define new subclass of functions with negative co-efficients and obtain the coefficient bounds, extreme points, inclusion relations, distortion bounds and many more properties for functions belonging to generalized class TS (r, s, β, X, Y).

Third Hankel Determinant for a Subfamily of Holomorphic Functions Related with Lemniscate of Bernoulli

The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szegö functional and the third Hankel determinant for a certain subclass SL∗u,v,α of holomorphic functions defined by the Carlson-Shaffer operator in the unit disk. Finally, for some special values of parameters, several corollaries were presented.

Some subclasses of analytic functions involving certain integral operator

Abstract In this paper, we introduce and investigate two new subclasses of analytic functions with bounded boundary and bounded radius rotations by using a certain p-valent operator which complies with the known Carlson–Shaffer operator for p = 1 {p=1} . Both of these operators are heavily explored and have various applications. We investigate some inclusions results and integral preserving properties. We also extend the Ruscheweyh and Sheil-Small convolution preserving properties in the context of these classes. We relate our finding with the existing known results found in the literature regarding this subject.

Third Hankel Determinant for a Subclass of Univalent Functions Associated with Lemniscate of Bernoulli

This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We find the upper bound of the Hankel determinant H3(1) for this subclass by applying the Carlson–Shaffer operator to it. The present work also deals with certain properties of this newly defined subclass, such as the upper bound of the Hankel determinant of order 3, coefficient estimates, etc.

A new parametric differential operator generalized a class of d'Alembert's equations

The studies in operator theory are attracting many researchers. The central aim of this investigation is to formulate a special parametric differential operator (PDO) based on the error function in the open unit disk. The suggested operator is related to the well-known Carlson–Shaffer operator and the differential operator due to Salagean. We express a class of analytic functions to study its performance in view of the geometric function theory. As application, we employ PDO to present the conformable d'Alembert's equation. We discuss the univalent solution of the suggested equation and study some of its geometric behaviours.

Certain subclasses of spiral-like functions associated with $ q $-analogue of Carlson-Shaffer operator

<abstract> <p>In this paper, making use of the $ q $-analogue of Carlson-Shaffer operator $ L_{q}\left(a, c\right) $ we introduce a new subclass of spiral-like functions and discuss some subordination results and Fekete-Szego problem for this generalized function class. Further, some known and new results which follow as special cases of our results are also mentioned.</p> </abstract>

ON SOME PROPERTIES OF A GENERALIZED CLASS OF CLOSE-TO-STARLIKE FUNCTIONS

In this paper, we consider a new class of close-to-starlike functions defined by the Carlson-Shaffer operator. Let denote the class of analytic univalent functions defined by then ifsatisfy the condition ,where and is a starlike function. Properties of the class such as the coefficient bounds, growth and distortion theorems and radius properties are investigated.

Fekete-Szego problem for a class of analytic functions defined by Carlson-Shaffer operator

In the present paper, authors study a Fekete-Szeg\"{o} problem for a class of analytic functions defined by Carlson-Shaffer operator. Relevant connections of the results presented here with various known results are briefly indicated.

Third-order differential subordination and superordination involving a fractional operator

Abstract The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

On Certain Subclasses of Analytic Functions Involving Carlson-Shaffer Operator and Related to Lemniscate of Bernoulli

The object of the present investigation is to solve the Fekete-Szegö problem and determine the sharp upper bound to the second Hankel determinant for a new class R(a,c) of analytic functions involving the Carlson-Shaffer operator in the unit disk. We also obtain a sufficient condition for normalized analytic functions in the unit disk to be in this class.

The Fekete–Szegö problem for a class of analytic functions defined by Carlson–Shaffer operator

AbstractIn the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

AbstractThe object of the present paper is to solve Fekete-Szegö problem and determine the sharp tipper bound to the second Hankel determinant for a certain class ℛ

Subordination preserving properties for multivalent functions associated with the Carlson-Shaffer operator

The purpose of the present paper is to investigate subordination and superordination properties for multivalent functions in the open unit disk associated with the Carlson-Shaffer operator with the sandwich-type theorems. MSC:30C45, 30C80.

The second Hankel determinant for a class of analytic functions associated with the Carlson-Shaffer operator

In this paper a new class of analytic functions, associated with the Carlson-Shaffer operator, is investigated. The sharp estimate for the Second Hankel determinant and class preserving transforms are studied.

On a class of analytic functions related to conic domains and associated with Carlson-Shaffer operator

Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigat inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.

On sandwich results for some subclasses of analytic functions involving certain linear operator

The purpose of this paper is to derive some subordination and superordination results for certain normalized analytic functions in the open unit disk, acted upon by Carlson–Shaffer operator. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

On some classes of p-valent functions involving Carlson–Shaffer operator

Let A ( p ) , p ∈ N , be a class of functions f : f ( z ) = z p + ∑ k = p + n ∞ a k z k analytic in the open unit disc E. We use Carlson–Shaffer operator for p-valent functions to define and study certain classes of analytic functions. Inclusion results, a radius problem and some other interesting properties are discussed.

On Sufficient Conditions for Certain Subclass of Analytic Functions Defined by Convolution

In the present investigation sufficient conditions are found for certain subclass of normalized analytic functions defined by Hadamard product. Differential sandwich theorems are also obtained. As a special case of this we obtain results involving Ruscheweyh derivative, Slgean derivative, Carlson-shaffer operator, Dziok-Srivatsava linear operator, Multiplier transformation.

ON SANDWICH THEOREMS FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING CARLSON-SHAFFER OPERATOR

The purpose of this present paper is to derive some subordination and superordination results involving Carlson–Shaffer operator for certain normalized analytic functions in the open unit disk.Relevant connections of the results, which are presented in the paper, with various known results are also considered.

On sandwich theorems for certain subclasses of analytic functions involving a linear operator

The purpose of this present paper is to derive some subordination and superordination results for certain normalized analytic functions involving complex order in the open unit disk, acted upon by Carlson–Shaffer operator. Relations of the results, which are obtained in this paper, with various known results are also presented. Mathematics subject classification (2000): 30C80, 30C45.