Results 21 to 30 of about 600 (109)
Strong Proximal Continuity and Convergence
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 In several situations the notion of uniform continuity can be strengthened to strong uniform continuity to produce interesting properties, especially in constrained problems. The same happens in the setting of proximity spaces. While a parallel theory for uniform and strong uniform convergence was recently developed, and a notion of proximal ...
Agata Caserta +3 more
wiley +1 more source
On bornological semigroups [PDF]
2015 International Conference on Research and Education in Mathematics (ICREM7), 2015 In this paper we introduce and study the concept of a bornological semigroup. This generalizes the theory of algebraic semigroup from the algebraic setting to the framework of bornological set. Working with bornological set allows to extend the scope of the latter theory considerably.
A.N. Imran, I. S. Rakhimov
openaire +1 more source
Caristi Type Coincidence Point Theorem in Topological Spaces
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 A generalized Caristi type coincidence point theorem and its equivalences in the setting of topological spaces by using a kind of nonmetric type function are obtained. These results are used to establish variational principle and its equivalences in d‐complete spaces, bornological vector space, seven kinds of completed quasi‐semimetric spaces equipped ...
Jiang Zhu +3 more
wiley +1 more source
Statistical Convergence in Function Spaces
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.
Agata Caserta +3 more
wiley +1 more source
Operator Ideals arising from Generating Sequences [PDF]
, 2011 In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be ...
Wong, Ngai-Ching
core +1 more source
An Ascoli theorem for sequential spaces
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 5, Page 303-315, 2001., 2001 Ascoli theorems characterize “precompact” subsets of the set of morphisms between two objects of a category in terms of “equicontinuity” and “pointwise precompactness,” with appropriate definitions of precompactness and equicontinuity in the studied category.
Gert Sonck
wiley +1 more source
Extensions defined using bornologies
Applied General Topology, 2013 Many extensions of a space X such that the remainder Y is closed can be constructed as B-extensions, that is, by defining a topology on the disjoint union X [ Y , provided there exists a map, satisfying some conditions, from a basis of Y into the family ...
Alessandro Caterino, M. Cristina Vipera
doaj +1 more source
Strictly barrelled disks in inductive limits of quasi‐(LB)‐spaces
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 727-732, 1996., 1996 A strictly barrelled disk B in a Hausdorff locally convex space E is a disk such that the linear span of B with the topology of the Minkowski functional of B is a strictly barrelled space. Valdivia′s closed graph theorems are used to show that closed strictly barrelled disk in a quasi‐(LB)‐space is bounded. It is shown that a locally strictly barrelled
Carlos Bosch, Thomas E. Gilsdorf
wiley +1 more source
Some remarks about Mackey convergence
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 4, Page 659-664, 1995., 1994 In this paper, we examine Mackey convergence with respect to K‐convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply property K; there are spaces having K‐ convergent sequences that are not Mackey convergent; there exists a space satisfying the Mackey convergence ...
Józef Burzyk, Thomas E. Gilsdorf
wiley +1 more source
On \(\beta\)-differentiability of norms
Journal of Numerical Analysis and Approximation Theory, 2004 In this note we give some characterizations for the differentiability with respect to a bornology of a continuous convex function. The special case of seminorms is treated.
Valeriu Anisiu
doaj +2 more sources