Related papers: There is at most one continuous invariant mean

We define a very general class of rational functions f:CP^1 --> CP^1 such that for every function f of this class, there exists a countable family of smooth curves \gamma_i and a critically finite hyperbolic function R such that the…

We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed…

We study the regularity of solutions of functional equations of a generalized mean value type. In this paper we give sufficient conditions for the regularity by using hypoellipticity which is a concept of the theory of partial differential…

We investigate stability and local minimizing properties of the Riemannian functional defined by the L^p norm of the curvature tensor on the space of Riemannian metrics on a closed manifold. Riemannian metrics with constant curvature and…

Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…

We prove continuity and surjectivity of the trace map onto $L_p$, from a space of functions of locally bounded variation, defined by the Carleson functional. The extension map is constructed through a stopping time argument. This extends…

We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…

We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form $p=w\rho$ is invariant under a 1-parameter family of continuous disformal transformations. In the…

We show that an arithmetic function which satisfies some weak multiplicativity properties and in addition has a non-decreasing or $\log$-uniformly continuous normal order is close to a function of the form $n\mapsto n^c$. As an application…

In this paper, we investigate the existence of nontrivial weak solutions to a class of elliptic equations ($\mathscr{P}$) involving a general nonlocal integrodifferential operator $\mathscr{L}_{\mathcal{A}K}$, two real parameters, and two…

We study Poisson's equation in the context of general state space Markov chains. For chains satisfying a contraction assumption w.r.t. a Wasserstein distance, we show that a solution exists for Lipschitz functions and investigate its…

We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are…

For a NIP theory $T$, a sufficiently saturated model $\mathfrak{C}$ of $T$, and an invariant (over some small subset of $\mathfrak{C}$) global type $p$, we prove that there exists a finest relatively type-definable over a small set of…

We study the Markov chain Monte Carlo (MCMC) estimator for numerical integration for functions that do not need to be square integrable w.r.t. the invariant distribution. For chains with a spectral gap we show that the absolute mean error…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…

We provide a general treatment of perturbations of a class of functionals modeled on convolution energies with integrable kernel which approximate the $p$-th norm of the gradient as the kernel is scaled by letting a small parameter…

In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…

The mean value theorem of calculus states that, given a differentiable function $f$ on an interval $[a, b]$, there exists at least one mean value abscissa $c$ such that the slope of the tangent line at $c$ is equal to the slope of the…

For a family {k_t | t \in I} of real C^2 functions defined on U (I, U -- open intervals) and satisfying some mild regularity conditions, we prove that the mapping I \ni t --> k_t^{-1}(\sum_{i=1}^n w_i k_t(a_i)) is a continuous bijection…

The $H~\mathrm{mod}~K$ theorem gives all possible periodic solutions in a $\Gamma-$equivariant dynamical system, based on the group-theoretical aspects. In addition, it classifies the spatio temporal symmetries that are possible. By the…