Search Results (19)

In this paper, we derive novel results concerning third-order differential subordinations for meromorphic functions, utilizing a newly defined linear operator that involves the inverse of the Legendre chi function in conjunction with the Mittag-Leffler identity. To establish these results, we introduce several families of admissible functions tailored to this operator and formulate sufficient conditions under which the subordinations hold. Our study presents three fundamental theorems that extend and generalize known results in the literature. Each theorem is accompanied by rigorous proofs and further supported by corollaries and illustrative examples that validate the applicability and sharpness of the derived results. In particular, we highlight special cases and discuss their implications through both analytical evaluations and graphical interpretations, demonstrating the strength and flexibility of our framework. This work contributes meaningfully to the field of geometric function theory by offering new insights into the behavior of third-order differential operators acting on p-valent meromorphic functions. Furthermore, the involvement of the Mittag-Leffler function positions the results within the broader context of fractional calculus, suggesting potential for applications in the mathematical modeling of complex and nonlinear phenomena. We hope this study stimulates further research in related domains. Full article

The present article aims to significantly improve geometric function theory by making an important contribution to p-valent meromorphic and analytic functions. It focuses on subordination, which describes the relationships of analytic functions. In order to achieve this, we utilize a technique that is based on the properties of differential subordination. This approach, which is one of the most recent developments in this field, may obtain a number of conclusions about differential subordination for p-valent meromorphic functions described by the new operator ${IH}_{p,\mathcal{q},s }^{\mathcal{j},p}\left({\nu }_1,\mathcal{n},\alpha ,\mathcal{l}\right)\mathcal{J}(\zeta )$  within the porous unit disk $\Delta$. Numerous mathematical and practical issues involving orthogonal polynomials, such as system identification, signal processing, fluid dynamics, antenna technology, and approximation theory, can benefit from the results presented in this article. The knowledge and comprehension of the unit’s analytical functions and its interacting higher relations are also greatly expanded by this text. 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

In this paper, we define a differential operator on an open unit disk $\Delta$ by using the novel Borel distribution (BD) operator and means of convolution. This operator is adopted to introduce new subclasses of p-valent functions through the principle of differential subordination, and we focus on some interesting inclusion relations of these classes. Additionally, some inclusion relations are derived by using the Bernardi integral operator. Moreover, relevant convolution results are established for a class of analytic functions on $\Delta$, and other results of analytic univalent functions are derived in detail. This study provides a new perspective for developing p-univalent functions with BD and offers valuable understanding for further research in complex analysis. 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

The aim of the present paper is to introduce and study some new subclasses of p-valent functions by making use of a linear q-differential Borel operator.We also deduce some properties, such as inclusion relationships of the newly introduced classes and the integral operator ${\mathcal{J}}_{\mu ,p}$. 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

The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution in the open unit disk U. Using the Hadamard product or convolution, function $f_s\left(z\right)$ is defined as involving an analytic p-valent function and generalized distribution expressed in terms of analytic p-valent functions. Neighborhood properties for functions $f_s\left(z\right)$ are established. Further, by applying a previously introduced linear transformation to $f_s\left(z\right)$ and using an extended Libera integral operator, a new generalized Libera-type operator is defined. Moreover, using the same linear transformation, subclasses of starlike, convex, close-to-convex and spiralike functions are defined and investigated in order to obtain geometrical properties that characterize the new generalized Libera-type operator. Symmetry properties are due to the involvement of the Libera integral operator and convolution transform. Full article

Nuclear power facilities are being expanded to satisfy expanding worldwide energy demand. Thus, uranium recovery from secondary resources has become a hot topic in terms of environmental protection and nuclear fuel conservation. Herein, a mesoporous biosorbent of a hybrid magnetic–chitosan nanocomposite functionalized with cysteine (Cys) was synthesized via subsequent heterogeneous nucleation for selectively enhanced uranyl ion (UO₂²⁺) sorption. Various analytical tools were used to confirm the mesoporous nanocomposite structural characteristics and confirm the synthetic route. The characteristics of the synthesized nanocomposite were as follows: superparamagnetic with saturation magnetization (M_S: 25.81 emu/g), a specific surface area (S_BET: 42.56 m²/g) with a unipore mesoporous structure, an amine content of ~2.43 mmol N/g, and a density of ~17.19/nm². The experimental results showed that the sorption was highly efficient: for the isotherm fitted by the Langmuir equation, the maximum capacity was about 0.575 mmol U/g at pH range 3.5–5.0, and Temperature (25 ± 1 °C); further, there was excellent selectivity for UO₂²⁺, likely due to the chemical valent difference. The sorption process was fast (~50 min), simulated with the pseudo-second-order equation, and the sorption half-time (t_1/2) was 3.86 min. The sophisticated spectroscopic studies (FTIR and XPS) revealed that the sorption mechanism was linked to complexation and ion exchange by interaction with S/N/O multiple functional groups. The sorption was exothermic, spontaneous, and governed by entropy change. Desorption and regeneration were carried out using an acidified urea solution (0.25 M) that was recycled for a minimum of six cycles, resulting in a sorption and desorption efficiency of over 91%. The as-synthesized nanocomposite’s high stability, durability, and chemical resistivity were confirmed over multiple cycles using FTIR and leachability. Finally, the sorbent was efficiently tested for selective uranium sorption from multicomponent acidic simulated nuclear solution. Owing to such excellent performance, the Cys nanocomposite is greatly promising in the uranium recovery field. Full article

In this paper, a new operator $D^{s}f$, with s a real number, is defined considering functions that belong to the known class of p-valent analytic functions in the open unit disk U. Applying this operator, a new subclass of p-valently analytic functions is introduced and some interesting subordination- and coefficient-related properties of the functions in this class are discussed. It is also shown that for certain values given to the parameters involved in the definition of the class, p-valently starlike and p-valently convex functions of certain orders can be obtained, respectively. Examples are also given as applications of the newly proven results. Full article

A class of p-valent analytic functions is introduced using the q-difference operator and the familiar Janowski functions. Several properties of functions in the class, such as the Fekete–Szegö inequality, coefficient estimates, necessary and sufficient conditions, distortion and growth theorems, radii of convexity and starlikeness, closure theorems and partial sums, are discussed in this paper. 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