Related papers: A Nonlinear Extension of Korovkin's Theorem

In this paper we extend Korovkin's theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function spaces. Several examples illustrating the theory are included.

In this paper we prove Korovkin type theorems for sequences of sublinear, monotone and weak additive operators acting on function spaces C(X); where X is a compact or a locally compact metric space. Our results are illustrated by a series…

This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…

In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their properties, a quantitative estimate for the nonlinear…

In this paper we prove analogues of Korovkin's theorem in the context of weakly nonlinear and monotone operators acting on Banach lattices of functions of several variables. Our results concern the convergence almost everywhere, the…

By extending the classical quantitative approximation results for positive and linear operators in $L^{p}([0, 1]), 1\le p \le +\infty$ of Berens and DeVore in 1978 and of Swetits and Wood in 1983 to the more general case of sublinear,…

We give a simple way to extend index-theoretical statements from partial differential operators with smooth coefficients to operators with coefficients of finite Sobolev order.

In this paper we obtain several extension properties for monotone and sublinear operators. The results obtained generalize those known for positive and linear operators.

We prove a noncommutative variant of Saskin's classical theorem -- on the connection between Choquet boundaries for function spaces and Korovkin sets -- for operator systems generating separable Type I C*-algebras. The main result implies…

In this paper we study extensions of commuting tuples of symmetric and isometric operators to commuting tuples of self-adjoint and unitary operators. Some conditions which ensure the existence of such extensions are presented. A…

This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L^p-functions, by means of positive linear…

We give some Korovkin-type theorems on convergence and estimates of rates of approximations of nets of functions, satisfying suitable axioms, whose particular cases are filter/ideal convergence, almost convergence and triangular…

The classical as well as non commutative Korovkin-type theorems deal with convergence of positive linear maps with respect to modes of convergences such as norm convergence and weak operator convergence. In this article, Korovkin-type…

In this note we will present an extension of the Krein-Rutman theorem for an abstract nonlinear, compact, positively 1-homogeneous, monotone non-decreasing operators on a Banach space and apply the result to many nonlinear elliptic partial…

In a seminal paper, Choquet introduced an integral formula to extend a monotone increasing setfunction on a sigma-algebra to a (nonlinear) functional on bounded measurable functions. The most important special case is when the setfunction…

This paper establishes an abstract Korovkin-type approximation theorem in general spaces, extending the framework of approximation theory to accommodate broader contexts. A critical result supporting this theorem is the proof that any…

We study monotone extension problems in the general framework of dual systems, without assuming separation. The paper develops a compact target-set formulation that includes multivalued operators as a special case and allows the initial set…

The concept of polytopes was a milestone in elementary integral group theory. In this article, we will extend the concept of contra-linearly stochastic lines to H-Positive Definite Monoids. We will show that by adding the Non-Gaussian…

We give some extensions of Mercer's theorem to continuous Carleman kernels inducing unbounded integral operators.

Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic…