46,620 Results Found

The acoustic activity in beam-shaped specimens made of cement is studied, assuming that the beams are loaded in three-point bending under a step-wise loading scheme. Attention is focused to the attenuation of the acoustic activity during the constant...

Silver–NHC (NHC = N-heterocyclic carbene) complexes play a special role in the field of transition-metal complexes due to (1) their prominent biological activity, and (2) their critical role as transfer reagents for the synthesis of metal-NHC c...

In this paper, we introduce the $\left(\rho ,q\right)$ -analog of the p-adic factorial function. By utilizing some properties of $\left(\rho ,q\right)$ -numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic $\left(\mathrm{\&rho}\right)$...

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 i...

In this note, we propose a new construction of cyclotomic p-adic L-functions that are attached to classical modular cuspidal eigenforms. This allows for us to cover most known cases to date and provides a method which is amenable to generalizations t...

Here, we study the extension of p-trigonometric functions $\mathrm{sinp}$ and $\mathrm{cosp}$ family in complex domains and p-hyperbolic functions $\mathrm{sinhp}$ and the $\mathrm{coshp}$ family in hyperbolic complex domains. These functions satisfy analogous relations as their classical coun...

In this paper, we establish a new ${(p,q)}^b$-integral identity involving the first-order ${(p,q)}^b$-derivative. Then, we use this result to prove some new ${(p,q)}^b$-integral inequalities related to Hermite–Hadamard inequalities for ${(p,q)}^b$-differentiable c...

In this paper, we introduce the concept of generalized Fourier series, generated by the p-trigonometric functions, namely cosp and sinp, recently introduced related to the generalized complex numbers systems. The aim of this study is to represent a p...

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 princip...

This article introduces $(p,q)$-analogs of the gamma integral operator and discusses their expansion to power functions, $(p,q)$-exponential functions, and $(p,q)$-trigonometric functions. Additionally, it validates other findings concerning $(p,q)$-analogs...

General asymptotic expansion of the $(p,k)$-gamma function is obtained and various approaches to this expansion are studied. The numerical precision of the derived asymptotic formulas is shown and compared. Results are applied to the analogues of digam...

The aim of this paper is to establish some new $(p,q)$ -calculus of Hermite–Hadamard inequalities for the double integral and refinements of the Hermite–Hadamard inequality for $(p,q)$ -differentiable convex functions.

In the present paper, we develop some implications leading to Carathéodory functions in the open disk and provide some new conditions for functions to be p-valent functions. This work also extends the findings of Nunokawa and others.

In this paper, we present the preliminaries of $(p,q)$ -calculus for functions of two variables. Furthermore, we prove some new Hermite-Hadamard integral-type inequalities for convex functions on coordinates over $[a,b]\times [c,$...

In this paper, we derive an identity of the q-definite integral of a continuous function f on a finite interval. We then use such identity to prove some new quantum integral inequalities for $(p,h)$-convex function. The results obtained in this paper g...

Making use of a post-quantum derivative operator, we define two classes of meromorphic analytic functions. For the considered family of functions, we aim to investigate the sharp bounds’ values in the case of the Fekete–Szegö problem. The study of th...

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 thi...

This research aims to present a linear operator ${\mathcal{L}}_{p,q}^{\rho ,\sigma ,\mu }f$ utilizing the q-Mittag–Leffler function. Then, we introduce the subclass of harmonic $(p,q)$-convex functions ${\mathcal{HT}}_{p,q}(\vartheta ,\mathcal{W},\mathcal{V})$ related to the Janowski function. For the...

In this paper, we establish several new $(p,q)$-integral identities involving $(p,q)$-integrals by using the definition of a $(p,q)$-derivative. These results are then used to derive $(p,q)$-integral Simpson- and Newton-type inequalities involving convex fun...

The goal of this article is to establish several new formulas and new results related to the Marichev-Saigo-Maeda fractional integral and fractional derivative operators which are applied on the $(p,q)$-extended Bessel function. The results are express...

In this paper, firstly we have established a new generalization of Hermite–Hadamard inequality via p-convex function and fractional integral operators which generalize the Riemann–Liouville fractional integral operators introduced by Rain...

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 a...

In this paper, we define $(p,q)$-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using $(p,q)$-integrals. Many results obtained in this paper provide significa...

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...

For evaluating the probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distributi...

In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using $(p,q)$-calculus. Moreover, we study some new $(p,q)$-Hermite–Hadamard inequalities for multiple integrals. Many results given in thi...

This article investigates fractional Hermite–Hadamard integral inequalities through the framework of Caputo fractional derivatives and MET-$(p,s)$-convex functions. In particular, we introduce new modifications to two classical fractional extensi...

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 o...

This paper presents direct and inverse theorems concerning the approximation of functions of several variables with bounded p-fluctuation using Walsh polynomials. These theorems provide estimates for the best approximation of such functions by polyno...

The present paper deals with a new differential operator denoted by $F_{p,t}^{\delta ,n,b,c,m,\beta }$, whose certain properties are deduced by using well-known earlier studies regarding differential inequalities and the Caratheodory function. The new introd...

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 pro...

In current manuscript, using Laguerre polynomials and $(p-q)$-Wanas operator, we identify upper bounds $\left|a_2\right|$ and $\left|a_3\right|$ which are first two Taylor-Maclaurin coefficients for a specific bi-univalent functions classes ${\mathcal{W}}_{\sum }(\eta ,\delta ,\lambda ,\sigma$...

In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for $\left(p,q\right)$-differentiable preinvex functions in the context of $\left(p,q\right)$-calculus. We also show that the...

Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type $\varphi \left(\zeta \right)=\zeta +{\displaystyle \sum _{j=2}^{\infty }}{d}_j{\zeta }^j$, which are bi-univalent in the disc $\{\zeta \in \mathbb{C}:|\zeta |<1\}$ involving the (p, q)-...

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of gene...

This paper studies a class of p-valent analytic functions in the open unit disk using a modified Tremblay operator based on the Riemann–Liouville fractional integral and derivative. We derive a series representation of the operator, which serve...

The motivation of the present article is to define the $(p-q)$-Wanas operator in geometric function theory by the symmetric nature of quantum calculus. We also initiate and explore certain new families of holormorphic and bi-univalent functions ${\mathcal{A}}_E(\lambda ,\sigma ,$...

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and sy...

In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. Th...

In this study, the generalized $(p,q)$-derivative operator is used to define a novel class of bi-univalent functions. For this class, we define constraints on the coefficients up to $|{\ell }_5|$. The functions are analyzed using a suitable operational method,...

In this paper, using the symmetrizing operator ${\delta }_{e_1{e}_2}^{2-l}$, we derive new generating functions of the products of $\left(p,q\right)$-modified Pell numbers with various bivariate polynomials, including Mersenne and Mersenne Lucas polynomials, Fibonacci and...

It is a familiar fact that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measuremen...

Integral operators of a fractional order containing the Mittag-Leffler function are important generalizations of classical Riemann–Liouville integrals. The inequalities that are extensively studied for fractional integral operators are the Hada...

In this paper, we first prove a new parameterized identity. Based on this identity we establish some parametrized Simpson-like type symmetric inequalities, for functions whose first derivatives are s-$tgs$-convex via Reimann–Liouville frational o...

We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as $(p,h)$ fractional type inequality and many others, as the $(p,h)$-c...

Since its discovery nearly 40 years ago, p53 has ascended to the forefront of investigated genes and proteins across diverse research disciplines and is recognized most exclusively for its role in cancer as a tumor suppressor. Levine and Oren (2009)...

The p53 protein is mutated in about 50% of human cancers. Aside from losing the tumor-suppressive functions of the wild-type form, mutant p53 proteins often acquire inherent, novel oncogenic functions, a phenomenon termed mutant p53 gain-of-function...

Wild-type p53 is known as “the guardian of the genome” because of its function of inducing DNA repair, cell-cycle arrest, and apoptosis, preventing the accumulation of gene mutations. TP53 is highly mutated in cancer cells and most TP53 hotspot mutat...

Müntz spaces satisfying the Müntz and gap conditions are considered. A Fourier approximation of functions in the Müntz spaces M_Λ,p of L_p functions is studied, where 1 < p < ∞. It is proven that up to an isomorphism and a change of variables, th...

A function that is holomorphic in a set E, in the complex plane, is called p-valent in E if, for every complex number, w, the equation f (z) = w has, at most, p roots in E. In this paper, we established some sufficient conditions for holomorphic func...