Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on varying spaces is natural. However, it seems that the first results in this direction have been obtained only recently, to the best of our knowledge. Here we consider sectorial operators on scales of Hilbert spaces. We def...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

By extending Ershov’s notion of a d-space from topological spaces to net convergence spaces, this paper details the d-completion of certain net convergence structures which are rich enough to support it. In particular, it is demonstrated that spaces which are embeddable into d-spaces which have iterated limits admit d-completions. The main result reported herein generalizes an existing procedur...

In this paper 1-dimensional and 2-dimensional top spaces with finite numbers of identities and connected Lie group components are characterized. MF-semigroups are determined. By using of the left-invariant vector fields of top spaces and their one-parameter subgroups, a relation between the Lie algebras of a class of top spaces and the Lie algebras of a class of Lie groups is determined. As a r...

In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of χ sequence spaces over p−metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform ∆2 condition, and we also discuss some topological properties of the resulting spaces of χ with respect to ideal structures which is solid and monotone. Hence, g...

ComK may be defined as the (cartesian closed) category of comonoids in chuK , or equivalently as dictionaries D for which any crossword over D has its main diagonal in D. Com2 resembles Top, ordinary topological spaces. Common to both are the Alexandroff posets and the Scott DCPOs, while the topological space R and the dual DCPO {−∞ < . . . < −2 < −1 < 0} jointly witness the incomparability of ...

the purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in banach spaces. our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

• A uniform approach to d -spaces, sober spaces and well-filtered is provided. The theory of (super) H-sober established. If H has property M, then the function space super equipped with topology pointwise convergence H-sober. a T 0 X iff its Smyth power P S ( ) category all reflective in Top . if M. In this paper, we provide spaces, develop general framework for dealing these spaces. concepts ...

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, ...

The purpose of this paper is to discuss some categorical properties of probabilistic convergence spaces. Its main theses are: (1) the construct P-PrTop of probabilistic pretopological spaces is the extensional topological hull of the construct FTPcs of FT -diagonal probabilistic convergence spaces for every triangular norm T ; (2) the construct P-PsTop of probabilistic pseudotopological spaces ...