The aim of this article is to characterize the saturation spaces that appear in inverse problems. Such spaces are defined for a regularization method and the rate of convergence of the estimation part of the inverse problem depends on their definition. Here we prove that it is possible to define these spaces as regularity spaces, independent of the choice of the approximation method. Moreover, ...

We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the qu...

In this paper, we generalize the concept of I statistical convergence, which is a recently introduced summability method, with an in…nite matrix of complex numbers and a modulus function. Lacunary sequences will also be included in our de…nitions. The name of our new method will be AI -lacunary statistical convergence with respect to a sequence of modulus functions. We also de…ne strongly AI -l...

Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. The second functor enables us to prove that the category CS can be embedded in the categor...

‎In this paper‎, ‎we generalize the proximal point algorithm to complete CAT(0) spaces and show‎ ‎that the sequence generated by the proximal point algorithm‎ $w$-converges to a zero of the maximal‎ ‎monotone operator‎. ‎Also‎, ‎we prove that if $f‎: ‎Xrightarrow‎ ‎]-infty‎, +‎infty]$ is a proper‎, ‎convex and lower semicontinuous‎ ‎function on the complete CAT(0) space $X$‎, ‎then the proximal...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

We identify and study an LDG-hybridizable Galerkin method, which is not an LDGmethod, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuousGalerkinmethods using polynomials of degree k ≥ 0 for both the potential as well as the flux, the order of convergence in L of both unknowns is k + 1. Moreover, both the ap...

The main objects of study are the homotopically stratified metric spaces introduced by Quinn. Closed unions of strata are shown to be stratified forward tame. Stratified fibrations between spaces with stratifications are introduced. Paths which lie in a single stratum except possibly at their initial points form a space with a natural stratification, and the evaluation map from that space of pa...

We propose a multiscale method based on a finite element heterogeneous multiscale method (in space) and the implicit Euler integrator (in time) to solve nonlinear monotone parabolic problems with multiple scales due to spatial heterogeneities varying rapidly at a microscopic scale. The multiscale method approximates the homogenized solution at computational cost independent of the small scale b...

Let {Xnk: k,n 1,2 be an array of row-wise independent random elements in a separable Banach space. Let {ank: k,n 1,2 be an array of Voo voo R+ real numbers such that /-k=l lank -< 1 and Ln=l exp(-a/A < for each c e where n V 2 Voo An kk=l ank. The complete convergence of l’k=l ank Xnk is obtained under varying moment and distribution conditions on the random elements. In particular, laws of lar...