Search Results (11)

This study introduces a new integral operator $I_{p,\mu }^{\delta }$ that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses: ${\Sigma }_p^{+}\left(\delta ,\mu ,\alpha \right)$, consisting of functions with nonnegative coefficients, and ${\Sigma }_p^{+}\left(\delta ,\mu ,\alpha ,c\right)$, which further fixes the second positive coefficient. For these classes, we establish a necessary and sufficient coefficient condition, which serves as the foundation for deriving a set of sharp results. These include accurate coefficient bounds, distortion theorems for functions and derivatives, and radii of starlikeness and convexity of a specific order. Furthermore, we demonstrate the closure property of the class ${\Sigma }_p^{+}\left(\delta ,\mu ,\alpha ,c\right)$, identify its extreme points, and then construct a neighborhood theorem. All the findings presented in this paper are sharp. To demonstrate the practical utility of our symmetric operator paradigm, we apply it to a canonical fractional electrodynamics problem. We demonstrate how sharp distortion theorems establish rigorous, time-invariant upper bounds for a solitary electrostatic potential and its accompanying electric field, resulting in a mathematically guaranteed safety buffer against dielectric breakdown. This study develops a symmetric and consistent approach to investigating the geometric characteristics of meromorphic multivalent functions and their applications in physical models. Full article

Certain characteristics of univalent functions with negative coefficients of the form $f\left(z\right)=z-{\sum }_{n=1}^{\infty }{a}_{2n}{z}^{2n},a_{2n}>0$ have been studied by Silverman and Berman. Pokley, Patil and Shrigan have discovered some insights into the Hadamard product of $\mathcal{P}$-valent functions with negative coefficients. S. M. Khairnar and Meena More have obtained coefficient limits and convolution results for univalent functions lacking a alternating type coefficient. In this paper, using the $\mathfrak{q}$-Difference operator, we developed the a subclass of meromorphically $\mathcal{P}$-valent functions with alternating coefficients. Additionally, we obtained multivalent function convolution results and coefficient limits. Full article

The idea of fuzzy differential subordination is a generalisation of the traditional idea of differential subordination that evolved in recent years as a result of incorporating the idea of fuzzy set into the field of geometric function theory. In this investigation, we define some general classes of p-valent analytic functions defined by the fuzzy subordination and generalizes the various classical results of the multivalent functions. Our main focus is to define fuzzy multivalent functions and discuss some interesting inclusion results and various other useful properties of some subclasses of fuzzy p-valent functions, which are defined here by means of a certain generalized Srivastava-Attiya operator. Additionally, links between the significant findings of this study and preceding ones are also pointed out. Full article

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 are extensively applied in many different areas of the mathematical, physical and engineering sciences. Here, in this article, we first apply the q-calculus in order to introduce the q-derivative operator ${\mathfrak{S}}_{\eta ,p,q}^{n,m}$. Secondly, by means of this q-derivative operator, we define an interesting subclass $\mathcal{T}{\aleph }_{\lambda ,p}^{n,m}(\eta ,\alpha ,\kappa )$ of the class of normalized analytic and multivalent (or p-valent) functions in the open unit disk $\mathbb{U}$. This p-valent analytic function class is associated with the class $\kappa$-$\mathcal{UCV}$ of $\kappa$-uniformly convex functions and the class $\kappa$-$\mathcal{UST}$ of $\kappa$-uniformly starlike functions in $\mathbb{U}$. For functions belonging to the normalized analytic and multivalent (or p-valent) function class $\mathcal{T}{\aleph }_{\lambda ,p}^{n,m}(\eta ,\alpha ,\kappa )$, we then investigate such properties as those involving (for example) the coefficient bounds, distortion results, convex linear combinations, and the radii of starlikeness, convexity and close-to-convexity. We also consider a number of corollaries and consequences of the main findings, which we derived herein. 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

A class of p-valent functions of complex order is defined with the primary motive of unifying the concept of prestarlike functions with various other classes of multivalent functions. Interesting properties such as inclusion relations, integral representation, coefficient estimates and the solution to the Fekete–Szegő problem are obtained for the defined function class. Further, we extended the results using quantum calculus. Several consequences of our main results are pointed out. Full article

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 functions are used with the help of the principle of subordination between analytic functions in order to define this subclass of analytic and p-valent functions. This function class generalizes various other subclasses of analytic functions, not only in classical Geometric Function Theory setting, but also some q-analogue of analytic multivalent function classes. We study and investigate some interesting properties such as sufficiency criteria, coefficient bounds, distortion problem, growth theorem, radii of starlikeness and convexity for this newly-defined class. Other properties such as those involving convex combination are also discussed for these functions. In the concluding part of the article, we have finally given the well-demonstrated fact that the results presented in this article can be obtained for the $(\mathfrak{p},q)$-variations, by making some straightforward simplification and will be an inconsequential exercise simply because the additional parameter $\mathfrak{p}$ is obviously unnecessary. Full article

The high affinity immunoglobulin E (IgE) receptor-FcεR1 is mainly expressed on the surface of effector cells. Cross-linking of IgE Abs bound to FcεR1 by multi-valent antigens can induce the activation of these cells and the secretion of inflammatory mediators. Since FcεR1 plays a central role in the induction and maintenance of allergic responses, this study aimed to investigate the association of FcεR1 with the allergic phenotype of Cε expression and cytokine and histamine release from peripheral leukocytes. Peripheral leukocytes from 67 allergic and 50 non-allergic subjects were used for genotyping analysis. Peripheral mononuclear cells (PBMCs) were used for Cε expression and ELISpot analysis, while polymorphonuclear cells (PMNs) were used for histamine release. The association between genotype polymorphism of the FcεR1α promoter region (rs2427827 and rs2251746) and allergic features of Cε expression and histamine were analyzed, and their effects on leukocytes function were compared with wild type. The genotype polymorphisms of FcεR1α promoter region with CT and TT in rs2427827 and TC in rs2251746 were significantly higher in allergic patients than in non-allergic controls. Patients with single nucleotide polymorphism (SNP) of FcεR1α promoter region had high levels of total IgE, mite-specific Der p 2 (Group 2 allergen of Dermatophagoides pteronyssinus)-specific IgE and IgE secretion B cells. The mRNA expression of FcεR1α was significantly increased after Der p2 stimulation in PBMCs with SNPs of the FcεR1α promoter region. Despite the increased Cε mRNA expression in PBMCs and histamine release from PMNs and the up-regulated mRNA expression of interleukin (IL)-6 and IL-8 secretions after Der p2 stimulation, there was no statistically significant difference between SNPs of the FcεR1α promoter region and the wild type. SNPs of FcεR1α promoter region were associated with IgE expression, IgE producing B cells, and increased Der p2-induced FcεR1α mRNA expression. These SNPs may be used as a disease marker for IgE-mediated allergic inflammation caused by Dermatophagoides pteronyssinus. Full article