113 Results Found

By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order $\alpha$ in the open unit disk $\mathbb{U}$ were introduced and studied from many different viewpoints and perspectives. In this p...

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. Var...

In this paper, the theory of symmetric q-calculus and conic regions are used to define a new subclass of q-starlike functions involving a certain conic domain. By means of this newly defined domain, a new subclass of normalized analytic functions in...

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 th...

The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated by several special cases and c...

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...

Starlike functions have gained popularity both in literature and in usage over the past decade. In this paper, our aim is to examine some useful problems dealing with q-starlike functions. These include the convolution problem, sufficiency criteria,...

By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk $\mathbb{U}$ . In particular, we find the Hankel determinant...

In this paper, we define a new family of q-starlike and q-convex functions related to the cardioid domain utilizing the ideas of subordination and the Sălăgean quantum differential operator. The primary contribution of this article is the d...

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 the...

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,...

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...

In this paper, two new classes of q-starlike functions in an open unit disc are defined and studied by using the q-fractional derivative. The class $\widetilde{S_q^{*}}\left(\alpha \right)$, $\alpha \in (-3,1]$, $q\in (0,1)$ generalizes the class $S_q^{*}$ of q-starlike f...

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...

In the present paper, using the q-difference operator, we introduce two classes of q-starlike functions and q-convex functions subordinate to secant hyperbolic functions. As functions in these classes have unique characteristic of missing coefficient...

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 shar...

In our present investigation, with the help of the basic (or q-) calculus, we first define a new domain which involves the Janowski function. We also define a new subclass of the class of q-starlike functions, which maps the open unit disk $\mathbb{U}$, given b...

In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications...

In this paper, we use q-derivative operator to define a new class of q-starlike functions associated with k-Fibonacci numbers. This newly defined class is a subclass of class $\mathcal{A}$ of normalized analytic functions, where class $\mathcal{A}$ is invariant...

Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is...

Owning to the importance and great interest of differential operators, two generalized differential operators, which may be symmetric or assymetric, are newly introduced in the present paper. Motivated by the familiar Jackson’s second and third...

This study introduces a subclass $S_{qs}^{*}$ 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-ord...

In this paper, we use the concept of quantum (or $\mathfrak{q}$-) calculus and define a $\mathfrak{q}$-analogous of a fractional differential operator and discuss some of its applications. We consider this operator to define new subclasses of uniformly $\mathfrak{q}$-starlike and $\mathfrak{q}$-convex...

This study introduces a novel subclass of q-starlike functions that is defined by the application of the q-difference operator and q-analogue of hyperbolic secant function. By making certain variations to the parameter “q”, the geometric interpretati...

In the present investigation, by using certain higher-order q-derivatives, the authors introduce and investigate several new subclasses of the family of multivalent q-starlike functions in the open unit disk. For each of these newly-defined function...

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 domai...

This article extends the study of q-versions of analytic functions by introducing and studying the association of starlike functions with trigonometric cosine functions, both defined in their q-versions. Certain coefficient inequalities like coeffici...

The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the neces...

By making use of q-calculus, we define and investigate several new subclasses of bi-univalent mappings related to the q-Noor integral operator. The coefficient bounds $|u_2|$ , $|u_3|$ and the Fekete–Szegő problem $$...

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...

The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals ar...

In this paper, the concepts of symmetric q-calculus and conic regions are used to define a new domain $\widetilde{{\mathsf{\Omega }}_{k,q,\alpha }},$ which generalizes the symmetric conic domains. By using the domain $\widetilde{{\mathsf{\Omega }}_{k,q,\alpha }}$, we define a new subclass of analytic and q-starlike functions i...

In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-con...

In this paper, we make use of the Riemann–Liouville fractional q-integral operator to discuss the class $S_{q,\delta }^{*}\left(\alpha \right)$ of univalent functions for $\delta >0,\alpha \in \mathbb{C}-\left\{0\right\}$, and $0<\left|q\right|<1$. Then, we develop convolution resul...

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 convolut...

The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in t...

This article defines a new class of meromorphic parabolic starlike functions in the punctured unit disc $D^{*}=\{z\in \mathbb{C}:0<|z|<1\}$ that includes fixed second coefficients of class $\mathcal{A}{}_{s,c}^d\left(\psi ,\tau ,\nu ,\eta \right)$ and the q- hypergeometric functions. For...

In this paper, we introduce and investigate a new subclass of analytic functions in the open unit disk by combining the $(\lambda ,q)$-fractional differintegral operator with the Euler generating function through the technique of subordination. This cl...

The main purpose of this investigation is to use quantum calculus approach and obtain the Bohr radius for the class of q-starlike (q-convex) functions of order $\alpha$ . The Bohr radius is also determined for a generalized class of q-Janowski st...

In this article, by utilizing the theory of quantum (or q-) calculus, we define a new subclass of analytic and multivalent (or p-valent) functions class ${\mathcal{A}}_p$, where class ${\mathcal{A}}_p$ is invariant (or symmetric) under rotations. The well-known class of Janowski...

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 d...

In this paper, we investigate new geometric properties of normalized analytic functions associated with the generalized Marcum Q-function. In particular, we focus on two analytic forms derived from a normalized derivative of a representation involvin...

In this paper, certain subclasses of meromorphic harmonic functions which are formulated using a q-differential operator are meticulously analyzed. Initially, two new subclasses $W_H^q(k;E,F)$ and $W_{\eta }^q(k;E,F)$ associated with the Janowski function with...

This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order $\gamma (\gamma \in \mathbb{C}\backslash \left\{0\right\})$ . This introduced a q-integral operator and certain subclasses of the newly introduced c...

In this paper, the harmonic function related to the q-Srivastava–Attiya operator is described to introduce a new class of complex harmonic functions that are orientation-preserving and univalent in the open-unit disk. We also cover some importa...

In this article we have defined two new subclasses of analytic functions $k-{\mathcal{S}}_q[A,B]$ and $k-{\mathcal{K}}_q[A,B]$ by using q-difference operator in an open unit disk. Furthermore, the necessary and sufficient conditions along with certain other useful pro...

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 transfor...

This article investigates the applications of the q-Carlson–Shaffer operator on subclasses of q-uniformly starlike functions, introducing the class $S{T}_q(m,c,d,\beta )$. The study establishes a necessary condition for membership in this class and...

Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic...

Emphasising their connection with shell-like star-like curves, this work investigates a new subclass of star-like functions defined by $\mathfrak{q}$-Fibonacci numbers and $\mathfrak{q}$-polynomials. We study the geometric and analytic properties of this subclass, including t...