Related papers: Nonlinear Versions of a Vector Maximal Principle

We consider Lurye (sometimes written Lur'e) systems whose nonlinear operator is characterised by a possibly multivalued nonlinearity that is bounded above and below by monotone functions. Stability can be established using a sub-class of…

In this paper, we establish a multi-parameter version of Bellow and Losert's Wiener-Wintner type ergodic theorem for dynamical systems not necessarily being commutative. More precisely, we introduce a weight class $\mathcal{D}$, which is…

In this paper, we establish a partial order principle, which is useful to deriving vector Ekeland variational principle (denoted by EVP). By using the partial order principle and extending Gerstewitz's functions, we obtain a vector EVP for…

The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also the methods do not require…

This paper deals with $\varepsilon$-efficient and $\varepsilon$-properly efficient points with respect to a co-radiant set in vector optimization problems. In the first part of the paper, we establish a new nonlinear separation theorem for…

In a previous paper, the authors introduced several vector space norms on the space of algebraic numbers modulo torsion which corresponded to the Mahler measure on a certain class of numbers and allowed the authors to formulate L^p Lehmer…

It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…

We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…

We prove that moduli spaces of semistable vector bundles of coprime rank and degree over a non-singular real projective curve are maximal real algebraic varieties if and only if the base curve itself is maximal. This provides a new family…

This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…

The paper establishes a version of the Hopf boundary point lemma for sections of a vector bundle over a manifold with boundary. This result may be viewed as a counterpart to the tensor maximum principle obtained by R. Hamilton in 1986.…

We prove a maximality theorem for one-parameter dynamical systems including multiplier one-parameter dynamical systems. Our main result is new even for one-parameter actions on commutative multiplier algebras including the algebra of…

We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…

Building on the notion of convex body domination introduced by Nazarov, Petermichl, Treil, and Volberg, we provide a general principle of bootstrapping bilinear estimates for scalar-valued functions into vector-valued versions with a…

We prove gradient estimates for solutions of the oblique derivative problem for a large class of elliptic and parabolic quasilinear PDEs. In particular, we expand on previous work of the author using a maximum principle argument. In…

Let $b$ be a non-degenerate symmetric (respectively, alternating) bilinear form on a finite-dimensional vector space $V$, over a field with characteristic different from $2$. In a previous work, we have determined the maximal possible…

In 1931, Banach proved that, far from being exceptional objects, the Weierstrass functions form a residual set in the space $\mathcal{C}[0,1]$ of continuous functions. Later on, in 1966, V. I. Gurariy showed that, except for zero, there is…

We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem…

We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of…

By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, which improves an earlier work of Brascamp-Lieb. We…