In this paper, assuming a natural sequentially compact conditionwe establish new fixed point theorems for Urysohn type maps between Fréchet spaces. In Section 2 we present new LeraySchauder alternatives, Krasnoselskii and Lefschetz fixed point theory for admissible type maps. The proofs rely on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence...

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

 In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...

We show that the unit ball of a full Hilbert C∗-module is sequentially compact in a certain weak topology if and only if the underlying C∗-algebra is finite dimensional. This provides an answer to the question posed in J. Chmieliński et al [Perturbation of the Wigner equation in inner product C∗-modules, J. Math. Phys. 49 (2008), no. 3, 033519].

We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about φ-types for φ NIP. In particular, we show that if M is a countable model, then an M -invariant φ-type is Borel definable. Also the space of M invariant φ-types is a Rosenthal compactum, which implies a number of topological tameness properties. Shelah introduced the indepen...

Motivated by questions in stability theory for hybrid dynamical systems, we establish some fundamental properties of the set of solutions to such systems. Using the notion of a hybrid time domain and general results on set and graphical convergence, we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and “upper semicontinuous” w...

Let $(X,d)$ be a compactmetric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all  continuous complex-valued functions $f$ on$X$ for which$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

Viglino defined a Hausdorff topological space to be C-compact if each closed subset of the space is anH-set in the sense of Velǐcko. In this paper, we study the class of Hausdorff spaces characterized by the property that each closed subset is an S-set in the sense of Dickman and Krystock. Such spaces are calledC-s-compact. Recently, the notion of strongly subclosed relation, introduced by Jose...