Q-starlike Functions Research Articles

Sharp Results for a New Class of Analytic Functions Associated with the q-Differential Operator and the Symmetric Balloon-Shaped Domain

In our current study, we apply differential subordination and quantum calculus to introduce and investigate a new class of analytic functions associated with the q-differential operator and the symmetric balloon-shaped domain. We obtain sharp results concerning the Maclaurin coefficients the second and third-order Hankel determinants, the Zalcman conjecture, and its generalized conjecture for this newly defined class of q-starlike functions with respect to symmetric points.

Third-order Hankel determinants for q-analogue analytic functions defined by a modified q-Bernardi integral operator

In this paper we define a Bernardi type quantum integral operator. It transforms the starlike univalent in the unit disk into a starlike region in it. We show that the upper-bound of the third-order Hankel determinant for classes of q-starlike functions is connected with a q-analogue integral operator, defined by a modified q-Bernardi integral operator. The Fekete-Szegö inequality of these classes is also investigated. Numerous well-known specific instances, examples and graphics are listed in the paper. The computations are done by Mathematica 13.3.

Certain inequalities related with Hankel and Toeplitz determinant for q-starlike functions

In the present article, we prove the sharp upper bounds for the second order Hankel determinants |H2(1)|,|H2(2)| and related functionals |a2a3−a4|, |a2a5−a3a4| for q-starlike functions. An upper bound for the third order Hankel determinant |H3(1)| along with the sharp upper bounds for Toeplitz determinant |Tm(n)|, where (m,n)∈{(2,2),(2,3),(3,1),(3,2)} are attained. Many known results are also obtained as corollaries of our main results.

New Applications of Fractional q-Calculus Operator for a New Subclass of q-Starlike Functions Related with the Cardioid Domain

Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional q-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional q-differintegral operator Dq,λmρ,σ and subordination, we define and develop a collection of q-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of q-starlike functions in the open unit disc U. Furthermore, we analyze novel findings with respect to the inverse function (μ−1) within the class of q-starlike functions in U. The findings in this paper are easy to understand and show a connection between present and past studies.

Applications of higher-order q-derivative operator for a new subclass of meromorphic multivalent q-starlike functions related with the janowski functions

Applications of higher-order q-derivative operator for a new subclass of meromorphic multivalent q-starlike functions related with the janowski functions

Applications of Fractional Differential Operator to Subclasses of Uniformly q-Starlike Functions

In this paper, we use the concept of quantum (or q-) calculus and define a q-analogous of a fractional differential operator and discuss some of its applications. We consider this operator to define new subclasses of uniformly q-starlike and q-convex functions associated with a new generalized conic domain, Λβ,q,γ. To begin establishing our key conclusions, we explore several novel lemmas. Furthermore, we employ these lemmas to explore some important features of these two classes, for example, inclusion relations, coefficient bounds, Fekete–Szego problem, and subordination results. We also highlight many known and brand-new specific corollaries of our findings.

Majorization problems for class of q-starlike functions

Majorization problems for class of q-starlike functions

The Properties of Meromorphic Multivalent q-Starlike Functions in the Janowski Domain

Many researchers have defined the q-analogous of differential and integral operators for analytic functions using the concept of quantum calculus in the geometric function theory. In this study, we conduct a comprehensive investigation to identify the uses of the Sălăgean q-differential operator for meromorphic multivalent functions. Many features of functions that belong to geometrically defined classes have been extensively studied using differential operators based on q-calculus operator theory. In this research, we extended the idea of the q-analogous of the Sălăgean differential operator for meromorphic multivalent functions using the fundamental ideas of q-calculus. With the help of this operator, we extend the family of Janowski functions by adding two new subclasses of meromorphic q-starlike and meromorphic multivalent q-starlike functions. We discover significant findings for these new classes, including the radius of starlikeness, partial sums, distortion theorems, and coefficient estimates.

Sharp Coefficient Bounds for a New Subclass of q-Starlike Functions Associated with q-Analogue of the Hyperbolic Tangent Function

In this study, by making the use of q-analogous of the hyperbolic tangent function and a Sălăgean q-differential operator, a new class of q-starlike functions is introduced. The prime contribution of this study covers the derivation of sharp coefficient bounds in open unit disk U, especially the first three coefficient bounds, Fekete–Szego type functional, and upper bounds of second- and third-order Hankel determinant for the functions to this class. We also use Zalcman and generalized Zalcman conjectures to investigate the coefficient bounds of a newly defined class of functions. Furthermore, some known corollaries are highlighted based on the unique choices of the involved parameters l and q.

On a Subfamily of q-Starlike Functions with Respect to m-Symmetric Points Associated with the q-Janowski Function

The main objective of this paper is to study a new family of analytic functions that are q-starlike with respect to m-symmetrical points and subordinate to the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego functional |a3−μa22| and convolution properties for the functions belonging to this new class. Several consequences of main results are also obtained.

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.

Hankel and Symmetric Toeplitz Determinants for a New Subclass of q-Starlike Functions

This paper considers the basic concepts of q-calculus and the principle of subordination. We define a new subclass of q-starlike functions related to the Salagean q-differential operator. For this class, we investigate initial coefficient estimates, Hankel determinants, Toeplitz matrices, and Fekete-Szegö problem. Moreover, we consider the q-Bernardi integral operator to discuss some applications in the form of some results.

Applications of the q-Derivative Operator to New Families of Bi-Univalent Functions Related to the Legendre Polynomials

By using the q-derivative operator and the Legendre polynomials, some new subclasses of q-starlike functions and bi-univalent functions are introduced. Several coefficient estimates and Fekete–Szegö-type inequalities for functions in each of these subclasses are obtained. The results derived in this article are shown to extend and generalize those in some earlier works.

Certain Coefficient Problems for q-Starlike Functions Associated with q-Analogue of Sine Function

This study introduces a subclass Sqs* of starlike functions associated with the q-analogue of the sine function defined in symmetric unit disk. This article comprises the investigation of sharp coefficient bounds, and the upper bound of the third-order Hankel determinant for this class. It also includes the findings of Zalcman and generalized Zalcman conjectures for functions of this class.

Duality on q-Starlike Functions Associated with Fractional q-Integral Operators and Applications

In this paper, we make use of the Riemann–Liouville fractional q-integral operator to discuss the class Sq,δ*(α) of univalent functions for δ>0,α∈C−{0}, and 0<|q|<1. Then, we develop convolution results for the given class of univalent functions by utilizing a concept of the fractional q-difference operator. Moreover, we derive the normalized classes Pδ,qζ(β,γ) and Pδ,q(β) (0<|q|<1, δ≥0,0≤β≤1,ζ>0) of analytic functions on a unit disc and provide conditions for the parameters q,δ,ζ,β, and γ so that Pδ,qζ(β,γ)⊂Sq,δ*(α) and Pδ,q(β)⊂Sq,δ*(α) for α∈C−{0}. Finally, we also propose an application to symmetric q-analogues and Ruscheweh’s duality theory.

Applications of Higher-Order q-Derivative to Meromorphic q-Starlike Function Related to Janowski Function

By making use of a higher-order q-derivative operator, certain families of meromorphic q-starlike functions and meromorphic q-convex functions are introduced and studied. Several sufficient conditions and coefficient inequalities for functions in these subclasses are derived. The results presented in this article extend and generalize a number of previous results.

Coefficient Inequalities for Multivalent Janowski Type q-Starlike Functions Involving Certain Conic Domains

In the current work, by using the familiar q-calculus, first, we study certain generalized conic-type regions. We then introduce and study a subclass of the multivalent q-starlike functions that map the open unit disk into the generalized conic domain. Next, we study potentially effective outcomes such as sufficient restrictions and the Fekete–Szegö type inequalities. We attain lower bounds for the ratio of a good few functions related to this lately established class and sequences of the partial sums. Furthermore, we acquire a number of attributes of the corresponding class of q-starlike functions having negative Taylor–Maclaurin coefficients, including distortion theorems. Moreover, various important corollaries are carried out. The new explorations appear to be in line with a good few prior commissions and the current area of our recent investigation.

Applications of a q-Differential Operator to a Class of Harmonic Mappings Defined by q-Mittag–Leffler Functions

Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of differential operators for harmonic functions with the help of basic concepts of quantum (q-) calculus operator theory; and introduce a new subclass of harmonic functions associated with the Janowski and q-Mittag–Leffler functions. We obtain several useful properties of the new class, such as necessary and sufficient conditions, criteria for analyticity, compactness, convexity, extreme points, radii of starlikeness, radii of convexity, distortion bounds, and integral mean inequality. Furthermore, we discuss some applications of this study in the form of some results and examples and highlight some known corollaries for verifying our main results presented in this investigation. Finally, the conclusion section summarizes the fact about the (p,q)-variations.

Certain New Subclass of Multivalent Q-Starlike Functions Associated with Q-Symmetric Calculus

In our present investigation, we extend the idea of q-symmetric derivative operators to multivalent functions and then define a new subclass of multivalent q-starlike functions. For this newly defined function class, we discuss some useful properties of multivalent functions, such as the Hankel determinant, symmetric Toeplitz matrices, the Fekete–Szego problem, and upper bounds of the functional ap+1−μap+12 and investigate some new lemmas for our main results. In addition, we consider the q-Bernardi integral operator along with q-symmetric calculus and discuss some applications of our main results.

Properties of q-Starlike Functions Associated with the q-Cosine Function

In this paper, our main focus is to define a new subfamily of q-analogue of analytic functions associated with the q-cosine function. Furthermore, we investigate some useful results such as the necessary and sufficient condition based on the convolution idea, growth and distortion bounds, closure theorem, convex combination, radii of starlikeness, extreme point theorem and partial sums results for the newly-defined functions class.