Search Results (36)

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 interpretation of the domain hyperbolic secant function has also been discussed. The primary objective is to investigate and establish key results on the differential subordination of various orders within this newly defined class. Furthermore, convolution properties are explored and coefficient bounds are derived for these functions. A deeper analysis of these coefficients bounds unveils intriguing geometric insights and significant mathematical problems. Full article

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. Full article

Geometric function theory, a subfield of complex analysis that examines the geometrical characteristics of analytic functions, has seen a sharp increase in research in recent years. In particular, by employing subordination notions, the contributions of different subclasses of analytic functions associated with innovative image domains are of significant interest and are extensively investigated. Since $\Re (1+sinh(z\left)\right)\ngtr 0,$ it implies that the class $S_{sinh}^{*}$ introduced in reference third by Kumar et al. is not a subclass of starlike functions. Now, we have introduced a parameter $\lambda$ with the restriction $0\le \lambda \le ln(1+\sqrt{2}),$ and by doing that, $\Re (1+sinh(\lambda z\left)\right)>0.$ The present research intends to provide a novel subclass of starlike functions in the open unit disk $\mathcal{U},$ denoted as $S_{sinh\lambda }^{*}$, and investigate its geometric nature. For this newly defined subclass, we obtain sharp upper bounds of the coefficients $a_n$ for $n=2,3,4,5.$ Then, we prove a lemma, in which the largest disk contained in the image domain of $q_0\left(z\right)=1+sinh\left(\lambda z\right)$ and the smallest disk containing $q_0\left(\mathcal{U}\right)$ are investigated. This lemma has a central role in proving our radius problems. We discuss radius problems of various known classes, including $S^{*}\left(\beta \right)$ and $\mathcal{K}\left(\beta \right)$ of starlike functions of order $\beta$ and convex functions of order $\beta$. Investigating $S_{sinh\lambda }^{*}$ radii for several geometrically known classes and some classes of functions defined as ratios of functions are also part of the present research. The methodology used for finding $S_{sinh\lambda }^{*}$ radii of different subclasses is the calculation of that value of the radius $r<1$ for which the image domain of any function belonging to a specified class is contained in the largest disk of this lemma. A new representation of functions in this class, but for a more restricted range of $\lambda$, is also obtained. Full article

In this paper, we first modify one of the most famous theorems on the principle of differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using this modified form, we generalize and improve several results, which appeared recently in the literature on the geometric function theory of complex analysis. We also prove some simple conditions for starlikeness, convexity, and the strong starlikeness of several one-parameter families of integral operators, including (for example) a certain $\mu$-convex integral operator and the familiar Bernardi integral operator. Full article

In this research, using the Poisson-type Miller-Ross distribution, we introduce new subclasses Sakaguchi type of star functions with respect to symmetric and conjugate points and discusses their characteristic properties and coefficient estimates. Furthermore, we proved that the class is closed by an integral transformation. In addition, we pointed out some new subclasses and listed their geometric properties according to specializing in parameters that are new and no longer studied in conjunction with a Miller-Ross Poisson distribution. Full article

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. Full article

Using the derivative operators’ $\mathfrak{q}$-analogs values, a wide variety of holomorphic function subclasses, $\mathfrak{q}$-starlike, and $\mathfrak{q}$-convex functions have been researched and examined. With the aid of fundamental ideas from the theory of $\mathfrak{q}$-calculus operators, we describe new $\mathfrak{q}$-operators of harmonic function ${\mathrm{H}}_{\varrho ,\chi ;\mathfrak{q}}^{\gamma }\mathfrak{F}\left(\varpi \right)$ in this work. We also define a new harmonic function subclass related to the Janowski and $\mathfrak{q}$-analog of Le Roy-type functions Mittag–Leffler functions. Several important properties are assigned to the new class, including necessary and sufficient conditions, the covering Theorem, extreme points, distortion bounds, convolution, and convex combinations. Furthermore, we emphasize several established remarks for confirming our primary findings presented in this study, as well as some applications of this study in the form of specific outcomes and corollaries. Full article

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 $|a_3-\mu a_2^2|$ and convolution properties for the functions belonging to this new class. Several consequences of main results are also obtained. Full article

In this paper, we make use of the concept of $q-$calculus in the theory of univalent functions, to obtain the bounds for certain coefficient functional problems of Janowski type starlike functions and to find the Fekete–Szegö functional. A similar results have been done for the function ${\wp }^{-1}.$ Further, for functions in newly defined class we determine coefficient estimates, distortion bounds, radius problems, results related to partial sums. Full article

We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski generalization of the Mittag-Leffler function. The family of functions introduced here is superordinated by a conic domain, which is impacted by the Janowski function. We obtain coefficient estimates and subordination conditions for starlikeness and Fekete–Szegö functional for functions belonging to the class. Full article

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 ${\mathcal{S}}^{\eta ,\mu }(F,H,\lambda )$, a representation theorem, the radius of starlikeness estimates, covering and distortion theorems and integral mean inequalities are obtained. Full article

Very recently, functions that map the open unit disc U onto a limaçon domain, which is symmetric with respect to the real axis in the right-half plane, were initiated in the literature. The analytic characterization, geometric properties, and Hankel determinants of these families of functions were also demonstrated. In this article, we present a q-analogue of these functions and use it to establish the classes of starlike and convex limaçon functions that are correlated with q-calculus. Furthermore, the coefficient bounds, as well as the third Hankel determinants, for these novel classes are established. Moreover, at some stages, the radius of the inclusion relationship for a particular case of these subclasses with the Janowski families of functions are obtained. It is worth noting that many of our results are sharp. Full article

In the past few years, many scholars gave much attention to the use of q-calculus in geometric functions theory, and they defined new subclasses of analytic and harmonic functions. While using the symmetric q-calculus in geometric function theory, very little work has been published so far. In this research, with the help of fundamental concepts of symmetric q-calculus and the symmetric q-Salagean differential operator for harmonic functions, we define a new class of harmonic functions connected with Janowski functions $\widetilde{{\mathcal{S}}_{\mathcal{H}}^0}\left(m,q,\mathcal{A},\mathcal{B}\right)$. First, we illustrate the necessary and sufficient convolution condition for $\widetilde{{\mathcal{S}}_{\mathcal{H}}^0}\left(m,q,\mathcal{A},\mathcal{B}\right)$ and then prove that this sufficient condition is a sense preserving and univalent, and it is necessary for its subclass $\widetilde{{\mathcal{TS}}_{\mathcal{H}}^0}\left(m,q,\mathcal{A},\mathcal{B}\right)$. Furthermore, by using this necessary and sufficient coefficient condition, we establish some novel results, particularly convexity, compactness, radii of q-starlike and q-convex functions of order $\alpha$, and extreme points for this newly defined class of harmonic functions. Our results are the generalizations of some previous known results. Full article

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. Full article

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. Full article