754 Results Found

The conditional Feynman integral provides solutions to integral equations equivalent to heat and Schrödinger equations. The Cameron–Martin translation theorem illustrates how the Wiener measure changes under translation via Cameron–M...

In this paper, we introduce a conditional double integral transform and a conditional double convolution product for a broad class of functionals defined on product abstract Wiener space. We first establish the existence of the conditional double int...

Spatial discretization of the stochastic semi-linear subdiffusion equations driven by fractionally integrated multiplicative space-time white noise is considered. The nonlinear terms f and $\sigma$ satisfy the global Lipschitz conditions and the linear grow...

This paper is devoted to exploring the mapping properties for the commutator ${\mu }_{\mathsf{\Omega },b}$ generated by Marcinkiewicz integral ${\mu }_{\mathsf{\Omega }}$ with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Unde...

In this paper, we introduce mixed-norm amalgam spaces ${(L^{\overrightarrow{p}},L^{\overrightarrow{s}})}^{\alpha }\left({\mathbb{R}}^n\right)$ and prove the boundedness of maximal function. Then, the dilation argument obtains the necessary and sufficient conditions of fractional integral operators’ bo...

We begin by introducing some function spaces $L_c^p\left({\mathbb{R}}^{+}\right),X_c^p\left(J\right)$ made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties of Mellin convolution operators mapping on these spaces,...

Differential and integral equations in reflexive Banach spaces have gained great attention and hve been investigated in many studies and monographs. Inspired by those, we study the existence of the solution to a delay functional integral equation of...

The integration requirements of laser ranging, imaging, and communication functions in space target detection have placed higher demands on system performance. This paper takes a modularly designed integrated laser ranging, imaging, and communication...

The paper investigates the regularization of solutions to nonlinear Volterra integral equations of the first kind, under the assumption that a solution exists and belongs to the space of continuous functions. The kernel of the equation is a different...

In this article, the $\alpha$-fractal interpolation function $f^{\alpha }$ corresponding to any function f belonging to the weighted Sobolev space ${\mathcal{W}}_{\rho }^{r,2}\left(I\right)$ is defined. The convergence of sequences of $\alpha$-fractal interpolation functions correspondin...

In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators ${\mathcal{M}}_{\mathsf{\Omega },\varphi }^{}$...

In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without ${\Delta }_2$ -conditions. We study the same problem in fuzzy Banach spaces and $\beta$ -ho...

Super-homogeneous functions including homogeneous functions, quasi-homogeneous functions, and several non-homogeneous functions are considered. Using the weight function method, the construction conditions of Hilbert-type multiple integral inequaliti...

There has been a considerable evolution of the theory of fractal interpolation function (FIF) over the last three decades. Recently, we introduced a multivariate analogue of a special class of FIFs, which is referred to as $\alpha$-fractal functions, from t...

We obtain the separability of mixed-norm Herz-slice spaces, establish a weak convergence on mixed-norm Herz-slice spaces, and get the boundedness of the Calderón–Zygmund operator T on mixed-norm Herz-slice spaces. Moreover, we get the ne...

We study fixed-point theorems of contractive mappings in b-metric space, cone b-metric space, and the newly introduced extended b-metric space. To generalize an existence and uniqueness result for the so-called ${\mathsf{\Phi }}_s$ functions in the b-metric space...

The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition sp...

We investigate a nonlinear integral equation derived through moment approximation from the individual-based representation of spatial logistic dynamics. The equation describes how the densities of pairs of individuals represented by points in continu...

In this paper, we investigate the generalized integral-type operator acting between the fractional Cauchy transform space and two classical analytic function spaces: the weighted Bloch space and the weighted Dirichlet space. For the operator acting i...

Multifunctional zoning is the primary basis for developing differentiated spatial planning systems and management policies of territorial spaces. The purpose of the paper is to generate an integrated multifunctional zoning scheme of the territorial s...

We investigate the existence of solutions for the Fredholm integral equation $\mathsf{\Phi }\left(\vartheta \right)=\mathcal{G}(\vartheta ,\mathsf{\Phi }\left(\vartheta \right))+{\int }_0^1\mathcal{F}(\vartheta ,\zeta ,\mathsf{\Phi }\left(\zeta \right))d\zeta ,$ for $\vartheta \in [0,1]$, in the setting of the modular function spaces...

Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as...

There arise some problems when we evaluate abstract Wiener integrals for functionals involving stochastic linear functionals combined with bounded operators on the abstract Wiener space (AWS). In this paper, we provide a certain condition on the boun...

In this paper, we introduce the notion of extended S-metric space of type $\left(\alpha ,\beta \right)$. This extension is a generalization of S-metric space, defined by employing two functions instead of considering a constant in the second condition of the S-me...

This paper considers a nonlinear fractional-order boundary value problem ${\hspace{0.25em}}^H{\mathbb{D}}_{a,g}^{{\alpha }_1,\beta ,\mu }x\left(t\right)+f(t,x\left(t\right){,}^H{\mathbb{D}}_{a,g}^{{\alpha }_2,\beta ,\mu }x\left(t\right))=0,$ for $t\in [a,b]$, ${\alpha }_1\in (1,2]$, ${\alpha }_2\in (0,1]$, $\beta \in [0,1]$ with appropriate in...

In this paper, we study the problem of the uniqueness of fixed points for operators defined on subspaces of the space of continuous functions $C[a,b]$ equipped with norms stronger than the supremum norm. We are particularly interested in Hölder sp...

This paper investigates a class of implicit neutral fractional integro-differential equations of Volterra–Fredholm type. The equations incorporate a tempered fractional derivative in the Caputo sense, along with both retarded (delay) and advanc...

This article delves into the spectral problem associated with a multiple differentiation operator that features an integral perturbation of boundary conditions of one specific type, namely, regular but not strengthened regular. The integral perturbat...

Time can be treated as a free parameter to isotropically stretch the tangent space. A trajectory, which matches the boundary conditions on its configuration, is adjusted so that velocity conditions are met. The modified trajectory is found by substit...

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subseq...

This paper introduces a novel F fixed-point iteration method that leverages Green’s function for solving the nonlinear Troesch problem in Banach spaces, which are symmetric spaces. The Troesch problem, characterized by its challenging boundary...

Covariant integral quantization with rotational $\mathrm{SO}\left(3\right)$ symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continu...

The study presented in this paper follows a line of research familiar for Geometric Function Theory, which consists in defining new integral operators and conducting studies for revealing certain geometric properties of those integral operators such...

The null-continuity of monotone measures is a weaker condition than continuity from below and possesses many special properties. This paper further studies this structure characteristic of monotone measures. Some basic properties of null-continuity a...

Among the few exactly solvable problems in theoretical physics, the 2D (two-dimensional) Newtonian free fall problem in Euclidean space is perhaps the least known as compared to the harmonic oscillator or the Kepler–Coulomb problems. The aim of...

This article notably targets the more general (extended) function spaces by investigating the regularity of the weak solutions or turbulent solutions to the Cauchy problem of the 3D magnetic Bénard system by converting it into mathematical sym...

In this paper, we establish certain $L^p$ bounds for several classes of rough Marcinkiewicz integrals over surfaces of revolution on product spaces. By using these bounds and using an extrapolation argument, we obtain the $L^p$ boundedness of these Marcink...

This paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due...

The aim of this research article is to explore the framework of tvs-cone b-metric spaces and establish some generalized common fixed point theorems for self mappings under generalized contractive conditions. To extend this theory, we introduce the no...

In the process of controlling an unmanned vehicle, it is practically important that under conditions of rapidly changing dynamic constraints, control laws be developed that would be optimal with respect to a given quality functional or a multicriteri...

We establish lower norm bounds for multivariate functions within weighted Lebesgue spaces, characterised by a summation of functions whose components solve a system of nonlinear integral equations. This problem originates in portfolio selection theor...

Treating architectural space as a relational structure that organizes practice, this study examines how the configuration of Aba Tibetan dwellings relates to behavioral, cognitive, and meaning-related responses. A standardized prototype from 75 surve...

This study introduces a novel class of fractional integral contractions within the framework of symmetric S-metric spaces. By embedding a Riemann–Liouville fractional integral ($\mathcal{RLFI}$) operator into an integral-type contractive condition, we offe...

In this article, a method is proposed for determining parameters of the exponentialy varying shear modulus of a functionally graded half-space. The method is based on the analytical solution of the problem of pure shear of an elastic functionally gra...

In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral frac...

This paper analyzes the Bagley–Torvik fractional-order equation with generalized fractional Hilfer derivatives of two orders for functions in Banach spaces under conditions expressed in the language of weak topology. We develop a comprehensive...

Emergency departments (EDs) operate under high-pressure and time-critical conditions in which spatial configuration plays a fundamental role in shaping workflow efficiency, staff coordination, and patient experience. Although Space Syntax has been in...

Churches are spaces designed with a unique acoustic identity, which is intimately connected to the oratory and musical needs of the historical period in which they were built. For instance, their typically long reverberation time is appropriate to sp...

During evolution, the development of bone was critical for many species to thrive and function in the boundary conditions of Earth. Furthermore, bone also became a storehouse for calcium that could be mobilized for reproductive purposes in mammals an...

In this study, we look at the wavelet basis for the nonparametric estimation of density and regression functions for continuous functional stationary processes in Hilbert space. The mean integrated squared error for a small subset is established. We...