Related papers: A regularity result for fixed points, with applica…
In this short note we capitalize on and complete our previous results on the regularity of the homogenized coefficients for Bernoulli perturbations by addressing the case of the Poisson point process, for which the crucial uniform local…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates…
We study the evolution of the fine-structure constant, $\alpha$, induced by non-linear density perturbations in the context of the simplest class of quintessence models with a non-minimal coupling to the electromagnetic field, in which the…
In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…
We study the regularity of weak solutions to a certain class of second order parabolic system under the only assumption of continuous coefficients. By using the $A-$caloric approximation argument, we claim that the weak solution $u$ to such…
In this paper we obtain some existence result of solution for general variational inequalities. As applications several coincidence and fixed point results are provided.
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
In this note, we showcase some recent results concerning the stickiness properties of nonlocal minimal graphs in the plane. To start with, the nonlocal minimal graphs in the plane enjoy an enhanced boundary regularity, since boundary…
In this paper we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric…
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
This paper develops a fixed-point iteration to solve the steady-state water flow equations in an urban water distribution network. The fixed-point iteration is derived upon the assumption of turbulent flow solutions and the validity of the…
The regularity theory of the Campanato space $\mathcal{L}^{(q,\lambda)}_k(\Omega)$ has found many applications within the regularity theory of solutions to various geometric variational problems. Here we extend this theory from…
In the literature on singular perturbation (Lavrentiev regularization) for the stable approximate solution of operator equations with monotone operators in the Hilbert space the phenomena of conditional stability and local well-posedness…
In this paper, we derive a stability result for $L_1$ and $L_{\infty}$ perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth,…