New Class Of Analytic Functions Research Articles

Starlike Functions of the Miller–Ross-Type Poisson Distribution in the Janowski Domain

In this paper, considering the various important applications of Miller–Ross functions in the fields of applied sciences, we introduced a new class of analytic functions f, utilizing the concept of Miller–Ross functions in the region of the Janowski domain. Furthermore, we obtained initial coefficients of Taylor series expansion of f, coefficient inequalities for f−1 and the Fekete–Szegö problem. We also covered some key geometric properties for functions f in this newly formed class, such as the necessary and sufficient condition, convex combination, sequential subordination and partial sum findings.

Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann–Liouville Fractional Integral Operator

In this research, we combine ideas from geometric function theory and fuzzy set theory. We define a new operator Dτ−λLα,ζm:A→A of analytic functions in the open unit disc Δ with the help of the Riemann–Liouville fractional integral operator, the linear combination of the Noor integral operator, and the generalized Sălăgean differential operator. Further, we use this newly defined operator Dτ−λLα,ζm together with a fuzzy set, and we next define a new class of analytic functions denoted by Rϝζ(m,α,δ). Several innovative results are found using the concept of fuzzy differential subordination for the functions belonging to this newly defined class, Rϝζ(m,α,δ). The study includes examples that demonstrate the application of the fundamental theorems and corollaries.

Hankel determinant for certain new classes of analytic functions associated the activation functions

In this article, we introduce two new classes of analytic functions Jtanh and JSG which are associated with the activation functions and defined by the ratio of analytic representations of convex and starlike functions. For functions in these classes, our primary goal is to determine the sharp upper bounds of second and third Hankel determinants.

On a New Ma-Minda Class of Analytic Functions Created by a Roulette Curve Formula

It is well known that there are two important classes of analytic functions of Ma-Minda type (MMT): Ma-Minda starlike and Ma-Minda convex functions. In this work, we suggest a new class of analytic functions, which is normalized in the open unit disk. The suggested class is generated by a roulette curve formula, which satisfies the symmetric behavior in the open unit disk. A roulette curve is shaped as the path outlined by the sum of two complex numbers, each affecting at a uniform rapidity in a circle. Special cases are illustrated involving special functions. Graphics of the curve are illustrated by using Mathematica 13.3.

Family of Analytic Functions with Negative Coefficients Involving $q-$Analogue of Multiplier Transformation Operator

We introduce a new class of analytic functions with negative coefficients by using the $q-$analogue of multiplier transformation operator. Coefficient inequalities, distortion theorems, closure theorems, and some properties involving the modified Hadamard products, radii of close-to-convexity, starlikeness, and convexity, and integral operators associated with functions belonging to this class are obtained.

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

In 2012, new classes of analytic functions on U×U¯ with coefficient holomorphic functions in U¯ were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok–Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok–Srivastava operator, we obtain a new operator Dz−γHmlα1,β1 that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok–Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential subordinations and superordinations concerning the operator Dz−γHmlα1,β1 are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties.

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.

Fekete-Szegö functional for a class of non-Bazilevic functions related to quasi-subordination

Abstract In this article, we study the Fekete-Szegö functional associated with a new class of analytic functions related to the class of bounded turning by using the principle of quasi-subordination. We derived the coefficient estimates including the classical Fekete-Szegö inequality for functions belonging to this class. We also improved some existing results.

Differential subordination and superordination studies involving symmetric functions using a $ q $-analogue multiplier operator

<abstract><p>The present investigation focus on applying the theories of differential subordination, differential superordination and related sandwich-type results for the study of some subclasses of symmetric functions connected through a linear extended multiplier operator, which was previously defined by involving the $ q $-Choi-Saigo-Srivastava operator. The aim of the paper is to define a new class of analytic functions using the aforementioned linear extended multiplier operator and to obtain sharp differential subordinations and superordinations using functions from the new class. Certain subclasses are highlighted by specializing the parameters involved in the class definition, and corollaries are obtained as implementations of those new results using particular values for the parameters of the new subclasses. In order to show how the results apply to the functions from the recently introduced subclasses, numerical examples are also provided.</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.

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.

The Fekete-Szegö estimates for a new class of analytic functions associated with the convolution

In the present investigation, we discuss the sharpness of the bound of the Fekete-Szego functional |a3 − µa2 2 | for the functions belonging to certain subclass Rǫ ν,Lg (ψ) of analytic functions by means of convolution. The significant and useful consequences with the relevance of this class with some known classes are also pointed out.

Geometric Properties for a New Class of Analytic Functions Defined by a Certain Operator

The aim of this paper is to define and explore a certain class of analytic functions involving the (p,q)-Wanas operator related to the Janowski functions. We discuss geometric properties, growth and distortion bounds, necessary and sufficient conditions, the Fekete–Szegö problem, partial sums, and convex combinations for the newly defined class. We solve the Fekete–Szegö problem related to the convolution product and discuss applications to probability distribution.

Some Properties of Janowski Symmetrical Functions

In our present work, the concepts of symmetrical functions and the concept of spirallike Janowski functions are combined to define a new class of analytic functions. We give a structural formula for functions in Sη,μ(F,H,λ), a representation theorem, the radius of starlikeness estimates, covering and distortion theorems and integral mean inequalities are obtained.

Certain New Class of Analytic Functions Defined by Using a Fractional Derivative and Mittag-Leffler Functions

Fractional calculus has a number of applications in the field of science, specially in mathematics. In this paper, we discuss some applications of fractional differential operators in the field of geometric function theory. Here, we combine the fractional differential operator and the Mittag-Leffler functions to formulate and arrange a new operator of fractional calculus. We define a new class of normalized analytic functions by means of a newly defined fractional operator and discuss some of its interesting geometric properties in open unit disk.

Properties of q-Symmetric Starlike Functions of Janowski Type

The word “symmetry” is a Greek word that originated from “symmetria”. It means an agreement in dimensions, due proportion, and arrangement; however, in complex analysis, it means objects remaining invariant under some transformation. This idea has now been recently used in geometric function theory to modify the earlier classical q-derivative introduced by Ismail et al. due to its better convergence properties. Consequently, we introduce a new class of analytic functions by using the notion of q-symmetric derivative. The investigation in this paper obtains a number of the latest important results in q-theory, including coefficient inequalities and convolution characterization of q-symmetric starlike functions related to Janowski mappings.

Bi-Univalent Condition Associated with the Modified Sigmoid Function

In the present work, the authors define and determine the bounds on the first few coefficients of the function f(Z) belonging to a new class of analytic functions with complex order associated with modified sigmoid function in the open unit disk.

Convolution Properties of q-Janowski-Type Functions Associated with (x,y)-Symmetrical Functions

The purpose of this paper is to define new classes of analytic functions by amalgamating the concepts of q-calculus, Janowski type functions and (x,y)-symmetrical functions. We use the technique of convolution and quantum calculus to investigate the convolution conditions which will be used as a supporting result for further investigation in our work, we deduce the sufficient conditions, Po´lya-Schoenberg theorem and the application. Finally motivated by definition of the neighborhood, we give analogous definition of neighborhood for the classes S˜qx,y(α,β) and K˜qx,y(α,β), and then investigate the related neighborhood results, which are also pointed out.

Certain Subclasses of Analytic Functions Associated with Generalized Telephone Numbers

The goal of this article is to contemplate coefficient estimates for a new class of analytic functions f associated with generalized telephone numbers to originate certain initial Taylor coefficient estimates and Fekete–Szegö inequality for f in the new function class. Comparable results have been attained for the function f−1. Further application of our outcomes to certain functions demarcated by convolution products with certain normalized analytic functions in the open unit disk are specified, and we obtain Fekete–Szegö variations for this new function class defined over Poisson and Borel distribution series.

Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions

The study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of functions An=f∈HU:fz=z+an+1zn+1+…,z∈U written simply A when n=1, the newly introduced class involves functions f∈A considered in the study due to their special properties. The aim of this paper is to present the outcomes of the study performed on the new class, which include a coefficient inequality, a distortion theorem and extreme points of the class. The starlikeness and convexity properties of this class are also discussed, and partial sums of functions from the class are evaluated in order to obtain class boundary properties.