Related papers: KYP Lemma for Non-Strict Inequalities and the asso…

The Bounded Real Lemma, i.e., the state-space linear matrix inequality characterization (referred to as Kalman-Yakubovich-Popov or KYP inequality) of when an input/state/output linear system satisfies a dissipation inequality, has recently…

We consider the Kalman - Yakubovich - Popov (KYP) inequality \[ \begin{pmatrix} X-A^* XA-C^*C & -A^*X B- C^*D\cr -B^*X A-D^* C & I- B^*X B-D^*D \end{pmatrix} \ge 0 \] for contractive operator matrices $ \begin{pmatrix} A&B\cr C &D…

For discrete-time causal linear input/state/output systems, the Bounded Real Lemma explains (under suitable hypotheses) the contractivity of the values of the transfer function over the unit disk for such a system in terms of the existence…

A trichotomy theorem for countable, stable, unsuperstable theories is offered. We develop the notion of a `regular ideal' of formulas and study types that are minimal with respect to such an ideal.

We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.

In this paper, we establish coincidence-like results in the case when the values of the correspondences are not convex. In order to do this, we define a new type of correspondences, namely properly quasi-convex-like. Further, we apply the…

For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…

Using as a main tool our recent result on the strict minimax inequality proved in [5], in this note we establish a multiplicity theorem for a problem of the type $$\cases{-K\left(\int_{\Omega}|\nabla u(x)|^2dx\right)\Delta u = h(x,u) & in…

A number of landmark existence theorems of nonlinear functional analysis follow in a simple and direct way from the basic separation of convex closed sets in finite dimension via elementary versions of the Knaster-Kuratowski-Mazurkiewicz…

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

We introduce a new minimax principle to prove the existence of multi-peak solutions to the Neumann problem of the $p$-Laplace equation $$ -\varepsilon^p \Delta_p u = u^{q-1} - u^{p-1} \ \ \text{in}\ \Omega,$$ where $\Om$ is a bounded domain…

We consider a Cauchy problem for a Hamilton--Jacobi equation with coinvariant derivatives of an order $\alpha \in (0, 1)$. Such problems arise naturally in optimal control problems for dynamical systems which evolution is described by…

In this paper, the problem of approximate symmetries of a class of non-linear reaction-diffusion equations called Kolmogorov-Petrovsky-Piskounov (KPP) equation is comprehensively analyzed. In order to compute the approximate symmetries, we…

This paper establishes three minimax theorems for possibly nonconvex functions on Euclidean spaces or on infinite-dimensional Hilbert spaces. The theorems also guarantee the existence of saddle points. As a by-product, a complete solution…

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…

This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…

We prove an easy version of the minimax theorem with no topological assumption. We deduce from it some domination criteria as well as an application to $p$-summing operators.

We use Toponogov's triangle comparison theorem from Riemannian geometry along with quantitative scale oriented variants of classical propagation of singularities arguments to obtain logarithmic improvements of the Kakeya-Nikodym norms…

We study the Neyman-Pearson theory for convex expectations (convex risk measures) on $L^{\infty}(\mu)$. Without assuming that the level sets of penalty functions are weakly compact, a new approach different from the convex duality method is…

The aim of this article is to establish new two-functions minimax inequalities extending classical results such as Simons' minimax theorem. Our results will be proved in a non-compact setting. We also prove, under general conditions, that…