Related papers: Nonlinear versions of Korovkin's abstract theorems

We study associate and double associate spaces of two-weighted Sobolev spaces of the first order on real half-line and we show that unlike the notion of duality the associativity is divided into two cases which we call "strong" and "weak"…

It is known that for every Banach space X and every proper WOT-closed subalgebra A of L(X), if A contains a compact operator then it is not transitive. That is, there exist non-zero x in X and f in X* such that f(Tx)=0 for all T in A. In…

Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong convergence) of the associated method with both perturbation and…

A basilar property and a useful tool in the theory of Sobolev spaces is the density of smooth compactly supported functions in the space $W^{k,p}(\R^n)$ (i.e. the functions with weak derivatives of orders $0$ to $k$ in $L^p$). On Riemannian…

We prove, assuming Souslin's Hypothesis, that each uncountable subspace of each zero-dimensional monotonically normal compact space contains an uncountable subset of the real line with either the metric, the Sorgenfrey, or the discrete…

We prove trace and extension results for Sobolev-type function spaces that are well suited for nonlocal Dirichlet and Neumann problems including those for the fractional $p$-Laplacian. Our results are robust with respect to the order of…

We prove a version of Axler-Zheng's Theorem on smooth bounded pseudoconvex domains in C^n on which the dbar-Neumann operator is compact.

We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints…

The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions for the following Schr\"odinger equation…

This article provides a power series summability based Korovkin type approximation theorem for any fuzzy sequence of positive linear operators. Using the notion of fuzzy modulus of smoothness, we also derive an associated approximation…

Given a compact of ${\bf R}^n$, there is always a doubling measure having it as its support. We use this fact to construct an integral operator that extends differentiable functions defined on any compact set of ${\bf R}^n$ to the whole of…

We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.

We construct a denotational model of linear logic, whose objects are all the locally convex and separated topological vector spaces endowed with their weak topology. The negation is interpreted as the dual, linear proofs are interpreted as…

In this note we revisit a result in [9], where we established nonlocal isoperimetric inequalities and the related embeddings for Besov spaces adapted to a class of H\"ormander operators of Kolmogorov-type. We provide here a new proof which…

The purpose of this paper is to provide tools for analyzing the compactness of sequences in Sobolev spaces, in particular if the sequence gets mapped onto a compact set by some nonlinear operator. Here, our focus lies on a very general…

We prove some existence (and sometimes also uniqueness) of weak solutions to some stationary equations associated to the complex Schr\''{o}dinger operator under the presence of a singular nonlinear term. Among other new facts, with respect…

We prove an abstract critical point theorem based on a cohomological index theory that produces pairs of nontrivial critical points with nontrivial higher critical groups. This theorem yields pairs of nontrivial solutions that are neither…

In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…

We study possible noncommutative (operator algebra) variants of the classical Hoffman-Rossi theorem from the theory of function algebras. In particular we give a condition on the range of a contractive weak* continuous homomorphism defined…

We discuss Lomonosov's proof of the Pontryagin-Krein Theorem on invariant maximal non-positive subspaces, prove the refinement of one theorem from \cite{OShT} on common fixed points for a group of fractional-linear maps of operator ball and…