scholarly journals Isometric approximation property of unbounded sets

2003 ◽  
Vol 43 (3-4) ◽  
pp. 359-372 ◽  
Author(s):  
Jussi Väisälä
Keyword(s):  
Approximation Property ◽  
Isometric Approximation

Isometric approximation property in euclidean spaces

2002 ◽  
Vol 128 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Jussi Väisälä
Keyword(s):  
Approximation Property ◽  
Euclidean Spaces ◽  
Isometric Approximation

scholarly journals Hyers-Ulam stability of isometries on bounded domains

2021 ◽  
Vol 19 (1) ◽  
pp. 675-689
Author(s):  
Soon-Mo Jung
Keyword(s):  
Approximation Property ◽  
Bounded Domains ◽  
Ulam Stability ◽  
Euclidean Spaces ◽  
Efficient Approach ◽  
Isometric Approximation

Abstract More than 20 years after Fickett attempted to prove the Hyers-Ulam stability of isometries defined on bounded subsets of R n {{\mathbb{R}}}^{n} in 1981, Alestalo et al. [Isometric approximation, Israel J. Math. 125 (2001), 61–82] and Väisälä [Isometric approximation property in Euclidean spaces, Israel J. Math. 128 (2002), 127] improved Fickett’s theorem significantly. In this paper, we will improve Fickett’s theorem by proving the Hyers-Ulam stability of isometries defined on bounded subsets of R n {{\mathbb{R}}}^{n} using a more intuitive and more efficient approach that differs greatly from the methods used by Alestalo et al. and Väisälä.

NORMAL FORMS FOR FUZZY LOGIC — AN APPLICATION OF KOLMOGOROV’S THEOREM

1996 ◽  
Vol 04 (04) ◽  
pp. 331-349 ◽  
Author(s):  
VLADIK KREINOVICH ◽  
HUNG T. NGUYEN ◽  
DAVID A. SPRECHER
Keyword(s):  
Neural Networks ◽  
Fuzzy Logic ◽  
Normal Form ◽  
Normal Forms ◽  
Approximation Property ◽  
Universal Approximation ◽  
Approximation Result ◽  
Logical Operations ◽  
Kolmogorov's Theorem

This paper addresses mathematical aspects of fuzzy logic. The main results obtained in this paper are: 1. the introduction of a concept of normal form in fuzzy logic using hedges; 2. using Kolmogorov’s theorem, we prove that all logical operations in fuzzy logic have normal forms; 3. for min-max operators, we obtain an approximation result similar to the universal approximation property of neural networks.

scholarly journals A Banach space without a basis which has the bounded approximation property

1987 ◽  
Vol 159 (0) ◽  
pp. 81-98 ◽  
Author(s):  
Stanislaw J. Szarek
Keyword(s):  
Banach Space ◽  
Approximation Property

scholarly journals Haagerup Approximation Property for Arbitrary von Neumann Algebras

2015 ◽  
Vol 51 (3) ◽  
pp. 567-603 ◽  
Author(s):  
Rui Okayasu ◽  
Reiji Tomatsu
Keyword(s):  
Approximation Property ◽  
Von Neumann Algebras ◽  
Von Neumann

scholarly journals Strong Approximation Property for Baer Orderings on ∗-Fields

1994 ◽  
Vol 165 (1) ◽  
pp. 1-22 ◽  
Author(s):  
K.H. Leung
Keyword(s):  
Strong Approximation ◽  
Approximation Property
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