New Subclass Of Analytic Functions Research Articles

Applications of a q-Integral Operator to a Certain Class of Analytic Functions Associated with a Symmetric Domain

In this article, our objective is to define and study a new subclass of analytic functions associated with the q-analogue of the sine function, operating in conjunction with a convolution operator. By manipulating the parameter q, we observe that the image of the unit disc under the q-sine function exhibits a visually appealing resemblance to a figure-eight shape that is symmetric about the real axis. Additionally, we investigate some important geometrical problems like necessary and sufficient conditions, coefficient bounds, Fekete-Szegö inequality, and partial sum results for the functions belonging to this newly defined subclass.

Second-order Hankel determinant for a subclass of analytic functions satisfying subordination condition connected with modified q-Opoola derivative operator

This paper introduces a new subclass of analytic functions employing the operator that was recently defined by the authors. The coefficients estimate $|a_s| (s = 2, 3)$ of the Taylor-Maclaurin series in this new class, as well as the Fekete-Szegö functional problems, have been derived. Furthermore, we obtained the sharp upper bound for the functional $|a_2a_4 − a_{3}^2|$ for functions belonging to this new subclass

On a Certain Subclass of Analytic Functions Defined by Bessel Functions

In this work, we introduce and investigate a new subclass of analytic functions in the open unit disc with negative coefficients. The object of the present paper is to determine the coefficient estimates, extreme points, integral means inequalities and subordination results for this class.

Third Hankel determinant for the class of analytic functions defined by Mathieu-type series related to a petal-shaped domain

UDC 517.5 We introduce a new subclass of analytic functions based on the Mathieu-type series related to a petal-shaped domain. We investigate the bounds of the initial coefficient estimates, the Fekete–Szegö inequality, and the Hankel determinant of order two and three.

A New Subclass of Analytic Functions Associated with the q-Derivative Operator Related to the Pascal Distribution Series

A new subclass TXq[λ,A,B] of analytic functions is introduced by making use of the q-derivative operator associated with the Pascal distribution. Certain properties of analytic functions in the subclass TXq[λ,A,B] are derived. Some known results are generalized.

INITIAL COEFFICIENT BOUNDS FOR A CLASS FUNCTIONS INVOLVING Q-SAL˘ AGEAN˘ DIFFERENTIAL OPERATOR

By making use of the q-analogue of famous S ̆al ̆agean differential operator, the authors define a new subclass of analytic functions with respect to other points. Fekete-Szeg ̈o inequality and initial coefficient bounds of a certain bi-starlike functions areobtained. Further several examples, remarks and applications of our results are enumerated.

SUBCLASS OF ANALYTIC FUNCTIONS ASSOCIATED WITH LINEAR OPERATOR

In this work, we introduce and study a new subclass of analytic functions defined by a linear operator and obtained coefficient estimates, growth and distortion theorems, radii of starlikeness, convexity and close-to-convexity are obtained. Furthermore, we obtained integral means inequalities for the class.

Sharp Coefficient and Hankel Problems Related to a Symmetric Domain

In the current article, we utilize the concept of subordination to establish a new subclass of analytic functions associated with a bounded domain that is symmetric about the real axis. By applying the convolution technique, we derive the necessary and sufficient condition, the radius of convexity for this recently introduced class. Furthermore, we prove the sharp upper bounds for the second-order Hankel determinants |H2,1ξ|,|H2,2ξ| and third-order Hankel determinant |H3,1ξ| for the functions ξ belonging to the newly defined class.

Bounds for Toeplitz Determinants and Related Inequalities for a New Subclass of Analytic Functions

In this article, we use the q-derivative operator and the principle of subordination to define a new subclass of analytic functions related to the q-Ruscheweyh operator. Sufficient conditions, sharp bounds for the initial coefficients, a Fekete–Szegö functional and a Toeplitz determinant are investigated for this new class of functions. Additionally, we also present several established consequences derived from our primary findings.

Applications of Fuzzy Differential Subordination for a New Subclass of Analytic Functions

This work is concerned with the branch of complex analysis known as geometric function theory, which has been modified for use in the study of fuzzy sets. We develop a novel operator Lα,λm:An→An in the open unit disc Δ using the Noor integral operator and the generalized Sălăgean differential operator. First, we develop fuzzy differential subordination for the operator Lα,λm and then, taking into account this operator, we define a particular fuzzy class of analytic functions in the open unit disc Δ, represented by Rϝλ(m,α,δ). Using the idea of fuzzy differential subordination, several new results are discovered that are relevant to this class. The fundamental theorems and corollaries are presented, and then examples are provided to illustrate their practical use.

Some Further Coefficient Bounds on a New Subclass of Analytic Functions

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass SQ of analytic functions with f′(z) subordinated to 1/(1−z)2 in the open unit disk. This class was introduced and studied by Răducanu. Our main aim is to give the sharp upper bounds of the second Hankel determinant H2,3f and the third Hankel determinant H3,1f for f∈SQ. This may help to understand more properties of functions in this class and inspire further investigations on higher Hankel determinants for this or other popular sub-classes of univalent functions.

Coefficient Results concerning a New Class of Functions Associated with Gegenbauer Polynomials and Convolution in Terms of Subordination

Gegenbauer polynomials constitute a numerical tool that has attracted the interest of many function theorists in recent times mainly due to their real-life applications in many areas of the sciences and engineering. Their applications in geometric function theory (GFT) have also been considered by many researchers. In this paper, this powerful tool is associated with the prolific concepts of convolution and subordination. The main purpose of the research contained in this paper is to introduce and study a new subclass of analytic functions. This subclass is presented using an operator defined as the convolution of the generalized distribution and the error function and applying the principle of subordination. Investigations into this subclass are considered in connection to Carathéodory functions, the modified sigmoid function and Bell numbers to obtain coefficient estimates for the contained functions.

Fuzzy differential subordination related to strongly Janowski functions

The research presented in this paper concerns the notion of geometric function theory called fuzzy differential subordination. Using the technique associated with fuzzy differential subordination, a new subclass of analytic functions related with the strongly Janowski-type functions is defined. The class is introduced by using a new operator defined by the convolution of the generalized Sălăgean differential operator and Choi integral linear operator. Certain inclusion relations are proved for this class by using the notion of fuzzy differential subordination. In addition, new fuzzy differential subordinations are obtained that characterize this class.

New Subclass of Analytic Functions Associated with Multiplier Transformation

New Subclass of Analytic Functions Associated with Multiplier Transformation

Certain subclass of analytic functions involving Hurwitz–Lerch zeta function

Making use of Integral operator involving the Hurwitz-Lerch zeta function, we introduce a new subclass of analytic functions defined in the open unit disk and investigate its various characteristics. Further we obtain some usual properties of the geometric function theory such as coefficient bounds, extreme points radius of starlikness and convexity, partial sums and neighbourhood results belonging to the class.

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.

New Subclass of Analytic Functions Associated with Fractional q− Differintegral Operator

In this paper, we have introduced a new subclass T α q,ξ,δ of univalent and analytic functions defined by fractional q− differintegral operator in the unit disc U = {z ∈ C : |z| < 1}. We obtained, among other results, coefficient inequality, convex set, extreme points, growth and distortion theorem, radii of a class of starlikeness, convexity, and neighborhood and Hadamard product for this subclass.

Subclass of analytic functions involving Erdély–Kober type integral operator in conic regions and applications to neutrosophic Poisson distribution

In this article we familiarize a new subclass of analytic functions comprising Erdély–Kober type integral operator linked with the Janowski functions. Further, we confer some significant geometric properties like necessary and sufficient condition, growth and distortion bounds convex combination, partial sums and Fekete–Szegő inequality for this newly demarcated class. Further we conferred Fekete–Szegő inequality related with neutrosophic Poisson distribution.

Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

The Atangana–Baleanu fractional integral and multiplier transformations are two functions successfully used separately in many recently published studies. They were previously combined and the resulting function was applied for obtaining interesting new results concerning the theories of differential subordination and fuzzy differential subordination. In the present investigation, a new approach is taken by using the operator previously introduced by applying the Atangana–Baleanu fractional integral to a multiplier transformation for introducing a new subclass of analytic functions. Using the methods familiar to geometric function theory, certain geometrical properties of the newly introduced class are obtained such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity, and close-to-convexity of functions belonging to the class. This class may have symmetric or assymetric properties. The results could prove interesting for future studies due to the new applications of the operator and because the univalence properties of the new subclass of functions could inspire further investigations having it as the main focus.

Applications of the Atangana–Baleanu Fractional Integral Operator

Applications of the Atangana–Baleanu fractional integral were considered in recent studies related to geometric function theory to obtain interesting differential subordinations. Additionally, the multiplier transformation was used in many studies, providing elegant results. In this paper, a new operator is defined by combining those two prolific functions. The newly defined operator is applied for introducing a new subclass of analytic functions, which is investigated concerning certain properties, such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and radii of starlikeness, convexity and close-to-convexity. This class may have symmetric or asymmetric properties. The results could prove interesting due to the new applications of the Atangana–Baleanu fractional integral and of the multiplier transformation. Additionally, the univalence properties of the new subclass of functions could inspire researchers to conduct further investigations related to this newly defined class.