We study a Γ -convergence problem related to a new characterization of Sobolev spaces W1,p(RN) (p > 1) established in H.-M. Nguyen [H.-M. Nguyen, Some new characterizations of Sobolev spaces, J. Funct. Anal. 237 (2006) 689–720] and J. Bourgain and H.-M. Nguyen [J. Bourgain, H.-M. Nguyen, A new characterization of Sobolev spaces, C. R. Acad. Sci. Paris, Ser. I 343 (2006) 75–80]. We can also hand...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

In this paper we make a survey of some recent developments of the theory of Sobolev spaces W (X, d,m), 1 < q < ∞, in metric measure spaces (X, d,m). In the final part of the paper we provide a new proof of the reflexivity of the Sobolev space based on Γ-convergence; this result extends Cheeger’s work because no Poincaré inequality is needed and the measure-theoretic doubling property is weakene...

In this paper, a new monotonicity, M(·, ·)-monotonicity,is introduced in Banach spaces, and the resolvent operator of an M(·, ·)monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with M(·, ·)monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the conver...

Since the turn of the century there have been several notions of convergence for subsets of metric spaces appear in the literature. Appearing in as a subset of these notions is the concepts of epi-convergence. In this paper we peresent definitions of epi-Cesaro convergence for sequences of lower semicontinuous functions from $X$ to $[-infty,infty]$ and Kuratowski Cesaro convergence of sequence...

The cascade algorithm with mask a and dilation M generates a sequence φ n , n = 1, 2,. .. , by the iterative process φ n (x) = α∈Z s a(α)φ n−1 (Mx − α) x ∈ R s , from a starting function φ 0 , where M is a dilation matrix. A complete characterization is given for the strong convergence of cascade algorithms in Sobolev spaces for the case in which M is isotropic. The results on the convergence o...

Our basic question: Restricting to covers of the sphere by a compact Riemann surface of a given type, do all such compose one connected family? Or failing that, do they fall into easily discerned components? The answer has often been “Yes!,” figuring in the connectedness of the moduli space of curves of genus g (geometry), Davenport’s problem (arithmetic) and the genus 0 problem (group theory)....

‎We introduce a higher dimensional Atkin-Lehner theory for‎ ‎Siegel-Parahoric congruence subgroups of $GSp(2g)$‎. ‎Old‎ ‎Siegel forms are induced by geometric correspondences on Siegel‎ ‎moduli spaces which commute with almost all local Hecke algebras‎. ‎We also introduce an algorithm to get equations for moduli spaces of‎ ‎Siegel-Parahoric level structures‎, ‎once we have equations for prime l...