Smoothing of uniformly continuous mappings in Lp spaces

1993 ◽  
Vol 54 (3) ◽  
pp. 957-967 ◽  
Author(s):  
I. G. Tsar'kov
Keyword(s):  
Lp Spaces ◽  
Continuous Mappings ◽  
Uniformly Continuous

scholarly journals A study of uniformities on the space of uniformly continuous mappings

2020 ◽  
Vol 18 (1) ◽  
pp. 1478-1490
Author(s):  
Ankit Gupta ◽  
Abdulkareem Saleh Hamarsheh ◽  
Ratna Dev Sarma ◽  
Reny George
Keyword(s):  
Uniform Space ◽  
Uniform Spaces ◽  
Continuous Mappings ◽  
Uniformly Continuous

Abstract New families of uniformities are introduced on UC(X,Y) , the class of uniformly continuous mappings between X and Y, where (X,{\mathcal{U}}) and (Y,{\mathcal{V}}) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.

scholarly journals On the extension of uniformly continuous mappings.

1968 ◽  
Vol 15 (1) ◽  
pp. 65-74 ◽  
Author(s):  
F. Grünbaum ◽  
E. H. Zarantonello
Keyword(s):  
Continuous Mappings ◽  
Uniformly Continuous

scholarly journals Paracompact-type mappings

2021 ◽  
Vol 102 (2) ◽  
pp. 62-66
Author(s):  
B.E. Kanetov ◽  
◽  
A.M. Baidzhuranova ◽  
Keyword(s):  
Uniform Space ◽  
Continuous Mapping ◽  
Uniform Spaces ◽  
Uniform Topology ◽  
Point Space ◽  
Continuous Mappings ◽  
Basic Concepts ◽  
Uniformly Continuous

Recently a new direction of uniform topology called the uniform topology of uniformly continuous mappings has begun to develop intensively. This direction is devoted, first of all, to the extension to uniformly continuous mappings of the basic concepts and statements concerning uniform spaces. In this case a uniform space is understood as the simplest uniformly continuous mapping of this uniform space into a one-point space. The investigations carried out have revealed large uniform analogs of continuous mappings and made it possible to transfer to uniformly continuous mappings many of the main statements of the uniform topology of spaces. The method of transferring results from spaces to mappings makes it possible to generalize many results. Therefore, the problem of extending some concepts and statements concerning uniform spaces to uniformly continuous mappings is urgent. In this article, we introduce and study uniformly R-paracompact, strongly uniformly R-paracompact, and uniformly R-superparacompact mappings. In particular, we solve the problem of preserving R-paracompact (respectively, strongly uniformly R-paracompact, uniformly R-superparacompact) spaces towards the preimage under uniformly R-paracompact (respectively, strongly uniformly R-paracompact, uniformly R-superparacompact) mappings.

scholarly journals A common fixed point theorem for semigroups of nonlinear uniformly continuous mappings with an application to asymptotic stability of nonlinear systems

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1949-1957
Author(s):  
Ahmed Soliman
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Common Fixed Point ◽  
Real Banach Space ◽  
Normal Structure ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Continuous Mappings ◽  
Uniformly Continuous ◽  
Common Fixed Point Theorem

In this paper, we study the existence of a common fixed point for uniformly continuous one parameter semigroups of nonlinear self-mappings on a closed convex subset C of a real Banach space X with uniformly normal structure such that the semigroup has a bounded orbit. This result applies, in particular, to the study of an asymptotic stability criterion for a class of semigroup of nonlinear uniformly continuous infinite-dimensional systems.

scholarly journals Stable Convergence Theorems for Products of Uniformly Continuous Mappings in Metric Spaces

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 156
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Stable Convergence ◽  
Convergence Theorems ◽  
Continuous Mappings ◽  
Computational Errors ◽  
Bounded Sets ◽  
Uniformly Continuous

We study the behavior of inexact products of uniformly continuous self-mappings of a complete metric space that is uniformly continuous and bounded on bounded sets. It is shown that previously established convergence theorems for products of non-expansive mappings continue to hold even under the presence of computational errors.

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