Brief survey of semigroup theory and its applications to evolution problems.
Brouwer degree, equivariant maps and tensor powers.
Browder-Fan fixed point theorem and related results
Browder-Krasnoselskii-type fixed point theorems in Banach spaces.
Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces.
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces.
Bukhvalov type characterizations of Urysohn operators
-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions
We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the -continuity property of these operators over Sobolev-type spaces of periodic functions.
-commuting maps and invariant approximations.
Calcul fonctionnel dans certains espaces de Besov
On montre que les fonctions qui opèrent, par composition a gauche, sur l’espace de Besov d’exposant , avec , dans l’espace euclidien de dimension , sont précisément les fonctions lipschitziennes.
Caractérisations de la convergence locale de la méthode des approximations successives
Caristi's fixed point theorem and its equivalences in fuzzy metric spaces
In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A. George , P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems. 64 (1994) 395-399]. Further, a direct simple proof of the equivalences among these theorems is provided.
Caristi's fixed point theorem in probabilistic metric spaces
In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems and Ekeland's variational principle for the class of (right) continuous and Archimedean t-norms. As an application, a partial answer to Kirk's problem in metric spaces is given.
Cauchy problems in weighted Lebesgue spaces
Global solvability and asymptotics of semilinear parabolic Cauchy problems in are considered. Following the approach of A. Mielke [15] these problems are investigated in weighted Sobolev spaces. The paper provides also a theory of second order elliptic operators in such spaces considered over , . In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed.
Characterization for the convergence of Krasnoselskij iteration for non-Lipschitzian operators.
Characterization of Globally Lipschitz Nemytskiĭ Operators Between Spaces of Set-Valued Functions of Bounded φ-Variation in the Sense of Riesz
Let (X,∥·∥) and (Y,∥·∥) be two normed spaces and K be a convex cone in X. Let CC(Y) be the family of all non-empty convex compact subsets of Y. We consider the Nemytskiĭ operators, i.e. the composition operators defined by (Nu)(t) = H(t,u(t)), where H is a given set-valued function. It is shown that if the operator N maps the space into (both are spaces of functions of bounded φ-variation in the sense of Riesz), and if it is globally Lipschitz, then it has to be of the form H(t,u(t)) = A(t)u(t)...
Characterization of globally Lipschitzian composition operators in the Banach space
We give a characterization of the globally Lipschitzian composition operators acting in the space
Characterization of the generators of semigroups which leave a convex set invariant
Characterizations of fixed points of nonexpansive mappings.
Characterizations of generalized monotone nonsmooth continuous maps using approximate Jacobians.