This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a contractivity property, stability and convergence are derived. These results are then applied to various schemes such as uncentered interpolatory linear schem...

connections between integral kernels of positivity preserving semigroups and suitable Lp contractivity properties are established. Then these questions are studied for the semigroups generated by -A + V and H,, the Dirichlet Laplacian for an open, connected region Q. As an application under a suitable hypothesis, Sobolev estimates are proved valid up to 352, of the form /n(x)1 ,< coo(x) lJHk,nl...

One of the generalizations of the Banach Fixed Point Theorem is due to Matkowski, who replaced contractivity by a weaker but still effective property. The aim of this note is to extend the contraction principle in this spirit for such semimetric spaces that are equipped with a natural generalization of the standard triangle inequality. The stability of fixed points is also investigated in this ...

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...

We said that φ is n-positive if φn is positive and that φ is completely positive if φn is positive for all n. The map φ is said to be n-bounded (resp., n-contractive) if ‖φn‖ ≤ c (resp., ‖φn‖ ≤ 1). The map φ is said to be completely bounded (resp., completely contractive) if ‖φ‖cb = supn‖φ‖n <∞ (resp., ‖φ‖cc = supn‖φn‖ ≤ 1). npositivity (resp., n-boundedness or n-contractivity) implies (n−1)-po...

Let LA, LB be the operators in divergence form associated with complex uniformly accretive matrix functions A,B on R. Take p > 1 and assume that for a.e. x ∈ R we have Re 〈A(x)ξ, Jpξ〉 > Cp|ξ| 2 for some Cp > 0 and all ξ ∈ C , where Jp(α + iβ) = α/p + iβ/p ′ for 1/p + 1/p′ = 1, and the same for B. Under this condition we prove that (f, g) 7→ 〈 ∇xe Af,∇xe Bg 〉 extends to a continuous bilinear emb...

*Correspondence: [email protected] 1Department of Quantitative Methods for Economics and Business, University of Granada, Granada, Spain Full list of author information is available at the end of the article Abstract Very recently, Roldán-López-de-Hierro and Shahzad introduced the notion of R-contractions as an extension of several notions given by different researchers (for instance, R-contractio...

Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential $U$ allowing for singularities. By modifying direct approach convergence in $L^2$ pioneered by F. H\'erau and developped Dolbeault, Mouhot Schmeiser, we show that converges exponentially fast topologies $L^2(d\mu)$ $L^2(W^* d\mu)$, where $\mu$ denotes invariant probability measure $...