Related papers: $\left(\varphi_1, \varphi_2\right)-$Variational pr…

We give a simple proof of the Baillon-Haddad theorem for convex functions defined on open and convex subsets of Hilbert spaces. We also state some generalizations and limitations. In particular, we discuss equivalent characterizations of…

In this paper, we prove the following result: Let $(H,\langle\cdot,\cdot\rangle)$ be a real Hilbert space, $B$ a ball in $H$ centered at $0$ and $\Phi:B\to H$ a $C^{1,1}$ function, with $\Phi(0)\neq 0$, such that the function $x\to \langle…

We prove results of existence of a solution (resp. existence and uniqness of a solution) for nonlinear differential equations of type $x'(t) +G(x,t) x(t) = F(x,t),$ in an abstract Banach subspace $X$ of the space of bounded real-valued…

In this paper we prove that if $f$ is a self-mapping of a nonempty subset $K$ of a normed space $X$ that satisfies some mild conditions, then the minimal displacement of large iterations $f^n$ always dominates that of $f$ along certain…

In this paper, we will see that the Cartesian product of two 2-Banach spaces is also 2-Banach space and discuss some properties of closed linear operator in linear 2-normed space. We also describe the concept of different types of…

We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…

Let $(x_n)$ be a normalized weakly null sequence in a Banach space and let $\varep>0$. We show that there exists a subsequence $(y_n)$ with the following property: $$\hbox{ if }\ (a_i)\subseteq \IR\ \hbox{ and }\ F\subseteq \nat$$ satisfies…

Let $Z$ be an $n$-dimensional Gaussian vector and let $f: \mathbb R^n \to \mathbb R$ be a convex function. We show that: $$\mathbb P \left( f(Z) \leq \mathbb E f(Z) -t\sqrt{ {\rm Var} f(Z)} \right) \leq \exp(-ct^2),$$ for all $t>1$, where…

We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations…

This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…

We consider weighted banach spaces of holomorphic functions on the upper half plane that are determined by $ \|f\|=\sup_{y>0,-\infty<x<\infty}p(y)|f(x+iy)|<\infty $ for a very large class of weight functions p. We completely solve the…

We prove an invariance principle for functions on a slice of the Boolean cube, which is the set of all vectors {0,1}^n with Hamming weight k. Our invariance principle shows that a low-degree, low-influence function has similar distributions…

We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Gordon, we show that the constant $2$ appearing in…

A "law of large numbers" for consecutive convex hulls for weakly dependent Gaussian sequences $\{X_n\}$, having the same marginal distribution, is extended to the case when the sequence $\{X_n\}$ has a weak limit. Let $\mathbb{B}$ be a…

In a recent paper, Madritsch and Tichy established Diophantine inequalities for the fractional parts of polynomial-like functions. In particular, for $f(x)=x^k+x^c$ where $k$ is a positive integer and $c>1$ is a non-integer, and any fixed…

In this paper, given two Banach spaces $X, Y$ and a $C^1$ functional $\Phi:X\times Y\to {\bf R}$, under general assumptions, we show that either $\Phi$ has a saddle-point in $X\times Y$ or, for each convex and dense set $S\subseteq Y$,…

A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…

We extend the definition of topological pressure to locally compact Hausdorff spaces, and we demonstrate a "variational principle" comparing the topological and measure theoretic pressures. Given a continuous $\mathbb{Z}_+^N$-action $T$…

The arbitrary functions principle says that the fractional part of $nX$ converges stably to an independent random variable uniformly distributed on the unit interval, as soon as the random variable $X$ possesses a density or a…

We extend the Palais-Smale condition to Keller's $C_c^1$-functionals on Fr\'{e}chet spaces. Using this condition together with Ekeland's variational principle, we obtain some results regarding the existence of minima. In this setting, we…