Search results for "paces"
showing 10 items of 496 documents
Sobolev embeddings, extensions and measure density condition
2008
AbstractThere are two main results in the paper. In the first one, Theorem 1, we prove that if the Sobolev embedding theorem holds in Ω, in any of all the possible cases, then Ω satisfies the measure density condition. The second main result, Theorem 5, provides several characterizations of the Wm,p-extension domains for 1<p<∞. As a corollary we prove that the property of being a W1,p-extension domain, 1<p⩽∞, is invariant under bi-Lipschitz mappings, Theorem 8.
On a Category of Extensional Fuzzy Rough Approximation L-valued Spaces
2016
We establish extensionality of some upper and lower fuzzy rough approximation operators on an L-valued set. Taking as the ground basic properties of these operators, we introduce the concept of an (extensional) fuzzy rough approximation L-valued space. We apply fuzzy functions satisfying certain continuity-type conditions, as morphisms between such spaces, and in the result obtain a category \(\mathcal{FRA}{} \mathbf{SPA}(L)\) of fuzzy rough approximation L-valued spaces. An interpretation of fuzzy rough approximation L-valued spaces as L-fuzzy (di)topological spaces is presented and applied for constructing examples in category \(\mathcal{FRA}{} \mathbf{SPA}(L)\).
The Besov capacity in metric spaces
2016
We study a capacity theory based on a definition of Haj{\l} asz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are $\gamma$-medians, for which we also prove a new version of a Poincar\'e type inequality.
Fixed point results for F-contractive mappings of Hardy-Rogers-type
2014
Recently, Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for self-mappings on complete metric spaces or complete ordered metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.
Categories of lattice-valued sets as categories of arrows
2006
In this paper we introduce a category X(A) which is a generalization of the category of lattice-valued subsets of sets Set(JCPos) introduced by us earlier. We show the necessary and sufficient conditions for X(A) to be topological over XxA.
A homotopy fixed point theorem in 0-complete partial metric space
2015
We generalize a result of Feng and Liu, on multi-valued contractive mappings, for studying the relationship between fixed point sets and homotopy fixed point sets. The presented results are discussed in the generalized setting of 0-complete partial metric spaces. An example and a nonlinear alternative of Leray-Schauder type are given to support our theorems.
Fixed point and homotopy results for mixed multi-valued mappings in 0-complete partial metric spaces*
2015
We give sufficient conditions for the existence of common fixed points for a pair of mixed multi-valued mappings in the setting of 0-complete partial metric spaces. An example is given to demonstrate the usefulness of our results over the existing results in metric spaces. Finally, we prove a homotopy theorem via fixed point results.
On product of p-sequential spaces
2016
Abstract The product of finitely many regular p-compact p-sequential spaces is p-compact p-sequential for any free ultrafilter p as it follows from [5] . In the paper is produced an example of a Hausdorff p-compact p-sequential space whose square is not p-sequential. It is also given an example of a space which is sP-radial, wP-radial, vwP-radial for any P ⊂ μ ( τ ) but its square is neither sP-radial nor wP-radial nor vwP-radial space.
Homomorphisms and composition operators on algebras of analytic functions of bounded type
2005
Abstract Let U and V be convex and balanced open subsets of the Banach spaces X and Y, respectively. In this paper we study the following question: given two Frechet algebras of holomorphic functions of bounded type on U and V, respectively, that are algebra isomorphic, can we deduce that X and Y (or X * and Y * ) are isomorphic? We prove that if X * or Y * has the approximation property and H wu ( U ) and H wu ( V ) are topologically algebra isomorphic, then X * and Y * are isomorphic (the converse being true when U and V are the whole space). We get analogous results for H b ( U ) and H b ( V ) , giving conditions under which an algebra isomorphism between H b ( X ) and H b ( Y ) is equiv…
Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions
2017
Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.