New Subclasses Of Analytic Functions Research Articles

Fractional Differential Operator Based on Quantum Calculus and Bi-Close-to-Convex Functions

In this article, we first consider the fractional q-differential operator and the λ,q-fractional differintegral operator Dqλ:A→A. Using the λ,q-fractional differintegral operator, we define two new subclasses of analytic functions: the subclass S*q,β,λ of starlike functions of order β and the class CΣλ,qα of bi-close-to-convex functions of order β. We explore the results on coefficient inequality and Fekete–Szegö problems for functions belonging to the class S*q,β,λ. Using the Faber polynomial technique, we derive upper bounds for the nth coefficient of functions in the class of bi-close-to-convex functions of order β. We also investigate the erratic behavior of the initial coefficients in the class CΣλ,qα of bi-close-to-convex functions. Furthermore, we address some known problems to demonstrate the connection between our new work and existing research.

Fekete-Szegӧ Functional for Classes X_q^n (φ) and Y_q^n (φ)

Two new subclasses of analytic functions are proposed by applying q-differential operator which is denoted as . Throughout this study, we acquired the initial coefficients and and the upper bound for the functional of the functions in the classes and .

Coefficient Bounds for Two Subclasses of Analytic Functions Involving a Limacon-Shaped Domain

In the current exploration, we defined new subclasses of analytic functions, namely Rlim(l,ν) and Clim(l,ν), defined by subordination linked with a Limacon-shaped domain. We found a few initial coefficient bounds and Fekete–Szegő inequalities for the functions in the above-stated new classes. The corresponding results have been derived for the function h−1. Additionally, we discuss the Poisson distribution as an application of our consequences.

Hankel determinants, Fekete-Szegö inequality, and estimates of initial coefficients for certain subclasses of analytic functions

<abstract><p>In this paper, we define new subclasses of analytic functions related to a modified sigmoid function and analytic univalent function. Then, we attempt to investigate the upper bounds of the third and fourth Hankel determinant in the special case. Further, bound on third Hankel determinant of its inverse function is also investigated. In addition, we attempt to obtain the Fekete-Szegö inequality for the classes. Then, we estimate the bounds of initial coefficients for the function belongs to some kind of new subclasses when its inverse function also belongs to these new subclasses.</p></abstract>

ON SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING q-DERIVATIVE OPERATOR WITH NEGATIVE COEFFICIENTS

The purpose of this work is to introduce and study new subclasses of analytic functions using a new q-derivative operator. This operator generalizes the operators introduced by Al-Oboudi, Catas, Cho and Kim, Cho and Srivastava, Maslina Darus and R W Ibrahim, Sˇalˇagean, Uralegaddi and Somanatha. We investigate coefficient bounds, growth, distortion and closure theorems for the functions belonging to these classes. We also give a result which unifies radii of close-toconvexity, starlikeness and convexity.

A note on convolution of Janowski type functions with q-derivative

Abstract The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with q-derivative. We also study certain a convolution conditions, and apply the convolution conditions to get sufficient condition and the neighborhood results related to the functions in the class 𝒮q(A, B, α).

Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators

In this paper, we introduced certain general new subclasses of analytic functions defined by the combination of two special operator which one of them derivative (Deniz-Orhan derivative operator) and other integral (Noor integral operators). For these classes coefficient estimates and the Fekete–Szegö inequality is completely solved.

Properties of a subclass of analytic functions defined by Riemann-Liouville fractional integral applied to convolution product of multiplier transformation and Ruscheweyh derivative

Abstract The contribution of fractional calculus in the development of different areas of research is well known. This article presents investigations involving fractional calculus in the study of analytic functions. Riemann-Liouville fractional integral is known for its extensive applications in geometric function theory. New contributions were previously obtained by applying the Riemann-Liouville fractional integral to the convolution product of multiplier transformation and Ruscheweyh derivative. For the study presented in this article, the resulting operator is used following the line of research that concerns the study of certain new subclasses of analytic functions using fractional operators. Riemann-Liouville fractional integral of the convolution product of multiplier transformation and Ruscheweyh derivative is applied here for introducing a new class of analytic functions. Investigations regarding this newly introduced class concern the usual aspects considered by researchers in geometric function theory targeting the conditions that a function must meet to be part of this class and the properties that characterize the functions that fulfil these conditions. Theorems and corollaries regarding neighborhoods and their inclusion relation involving the newly defined class are stated, closure and distortion theorems are proved, and coefficient estimates are obtained involving the functions belonging to this class. Geometrical properties such as radii of convexity, starlikeness, and close-to-convexity are also obtained for this new class of functions.

Certain Inclusion Properties for the Class of q-Analogue of Fuzzy α-Convex Functions

Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis. We introduce the family of linear q-operators and define various classes associated with these operators. The inclusion results and various integral properties are the main investigations of this article.

On a New Subclass of q-Starlike Functions Defined in q-Symmetric Calculus

Geometric function theory combines geometric tools and their applications for information and communication analysis. It is also successfully used in the field of advanced signals, image processing, machine learning, speech and sound recognition. Various new subclasses of analytic functions have been defined using quantum calculus to investigate many interesting properties of these subclasses. This article defines a new class of q-starlike functions in the open symmetric unit disc ∇ using symmetric quantum calculus. Extreme points for this class as well as coefficient estimates and closure theorems have been investigated. By fixing several coefficients finitely, all results were generalized into families of analytic functions.

On New Subclasses of Analytic Functions Involving (p,q)-Derivatives

Objective: The objectives of the present study are to introduce some new subclasses of analytic functions involving (p,q)-derivatives by using subordination. We derive Fekete-Szegö inequalities for the functions belonging to the new subclasses. Method: Using the concept of (p,q)-derivative of a function and the subordination principle between analytic functions we introduce and study new subclasses. Findings: The Fekete-Szegö problem may be considered as one of the most important results about univalent functions. It was introduced by Fekete-Szegö in 1933. Coefficient estimates for the second and third coefficients of functions belonging to class of analytic functions with specific geometric properties were obtained. We obtain the Fekete-Szegö inequalities for functions belonging to the new subclasses. Moreover, some special cases of the established results are discussed. Novelty: The results of the paper are new and significantly contribute to the existing literature on the topic. Keywords: Analytic functions; Subordination; q-calculus; Fekete-Szegö inequalities; (p; q)-derivative operator

Fekete-Szegö Inequalities for Some Certain Subclass of Analytic Functions Defined with Ruscheweyh Derivative Operator

In our present investigation, we introduce and study some new subclasses of analytic functions associated with Ruscheweyh differential operator Dr. We obtain a Fekete–Szegö inequality for certain normalized analytic function defined on the open unit disk for which Drl′(z)ϑzDrl′(z)Drl(z)1−ϑ≺ez (0≤ϑ≤1) lies in a starlike region with respect to 1 and symmetric with respect to the real axis. As a special case of this result, the Fekete–Szegö inequality for a class of functions defined through Poisson distribution series is obtained.

Bi-Univalent Problems Involving Generalized Multiplier Transform with Respect to Symmetric and Conjugate Points

In the present article, using the subordination principle, the authors employed certain generalized multiplier transform to define two new subclasses of analytic functions with respect to symmetric and conjugate points. In particular, bi-univalent conditions for function f(z) belonging to these new subclasses and their relevant connections to the famous Fekete-Szegö inequality |a3−va22| were investigated using a succinct mathematical approach.

Results on Univalent Functions Defined by q-Analogues of Salagean and Ruscheweh Operators

In this paper, we define and discuss properties of various classes of analytic univalent functions by using modified q-Sigmoid functions. We make use of an idea of Salagean to introduce the q-analogue of the Salagean differential operator. In addition, we derive families of analytic univalent functions associated with new q-Salagean and q-Ruscheweh differential operators. In addition, we obtain coefficient bounds for the functions in such new subclasses of analytic functions and establish certain growth and distortion theorems. By using the concept of the (q, δ)-neighbourhood, we provide several inclusion symmetric relations for certain (q, δ)-neighbourhoods of analytic univalent functions of negative coefficients. Various q-inequalities are also discussed in more details.

Hankel Determinants for a New Subclasses of Analytic Functions Involving a Linear Operator

Using the operator L(a, c) defined by Carlson and Shaffer, we defined a new subclass of analytic functions ML(λ, a, c). The well known Fekete-Szegö problem, upper bound of Hankel determinant of order two, and coefficient bound of the fourth coefficient is determined. Our investigation generalises some previous results obtained in different articles.

A Study on Certain Subclasses of Analytic Functions Involving the Jackson q-Difference Operator

We introduce two new subclasses of analytic functions in the open symmetric unit disc using a linear operator associated with the q-binomial theorem. In addition, we discuss inclusion relations and properties preserving integral operators for functions in these classes. This paper generalizes some known results, as well as provides some new ones.

Some Inclusion Relations of Certain Subclasses of Strongly Starlike, Convex and Close-to-Convex Functions Associated with a Pascal Operator

This paper studies some inclusion properties of some new subclasses of analytic functions in the open symmetric unit disc U that are associated with the Pascal operator. Furthermore, the integral-preserving properties in a sector for these subclasses are also investigated.

The Sufficient and Necessary Conditions for the Poisson Distribution Series to Be in Some Subclasses of Analytic Functions

In this paper, we introduce new subclasses of analytic functions in the open unit disc. Furthermore, the necessary and sufficient conditions for the Poisson distribution series to be in these new subclasses are found.

Generalization of k-Uniformly Starlike and Convex Functions Using q-Difference Operator

In this article we have defined two new subclasses of analytic functions k−Sq[A,B] and k−Kq[A,B] by using q-difference operator in an open unit disk. Furthermore, the necessary and sufficient conditions along with certain other useful properties of these newly defined subclasses have been calculated by using q-difference operator.

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.