Related papers: The Fermat-Torricelli problem in normed spaces
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
The aim of this paper is to to show the admissibility of some class of Frechet spaces (see Definition 2.3). In particular, this generalizes the main results of [3]. As an application, we show the admissibility of a large class modular…
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
The objective of this manuscript is to introduce and develop the concept of a generalized $\theta$-parametric metric space-a novel extension that enriches the modern metric fixed point theory. We study of its fundamental properties,…
We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
In this work we study weighted total least squares problems on infinite dimensional spaces. We show that in most cases this problem does not admit a solution (except in the trivial case) and then, we consider a regularization on the…
It is proved the existence of nonclassical solutions of the Neumann and Poincare problems for generalizations of the Laplace equation in anisotropic and nonhomogeneous media in almost smooth domains with arbitrary boundary data that are…
The equivalence problem of curves with values in a Riemannian manifold, is solved. The domain of validity of Frenet's theorem is shown to be the spaces of constant curvature. For a general Riemannian manifold new invariants must thus be…
In this paper, we introduce cone normed linear space, study the cone convergence with respect to cone norm. Finally, we prove the completeness of a finite dimensional cone normed linear space.
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…
We investigate the differences and similarities of the Dirichlet problem of the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski space. Although the solvability of the Dirichlet problem follows standards…
Following the definition of perturbed metric space, in this paper, some fixed point theorems are established for $ F $-perturbed mappings in complete perturbed metric spaces and justify the result by counter example. Finally, an application…
We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular topological spaces we establish a variational principle for saddle points. Well-posedness of saddle…
The Nontrivial Projection Problem asks whether every finite-dimensional normed space of dimension greater than one admits a well-bounded projection of non-trivial rank and corank or, equivalently, whether every centrally symmetric convex…
The aim of this paper is to discuss Penot's problem on a generalization of Caristi's fixed point theorem. We settle this problem in the negative and we present some new theorems on the existence of fixed points of set-valued mappings in…
In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, which can be seen…
The Fermat-Weber location problem requires finding a point in $\mathbb{R}^n$ that minimizes the sum of weighted Euclidean distances to $m$ given points. An iterative solution method for this problem was first introduced by E. Weiszfeld in…
In this paper we formulate and solve extremal problems in the d-dimensional Euclidean space and further in hypergraphs, originating from problems in stoichiometry and elementary linear algebra. The notion of affine simplex is the bridge…