Optimal Approximation and Error Bounds in Normed Spaces

1968 ◽  
pp. 283-283
Author(s):  
Jean Meinguet
Keyword(s):  
Error Bounds ◽  
Optimal Approximation ◽  
Normed Spaces

Optimal approximation and error bounds in seminormed spaces

1967 ◽  
Vol 10 (4) ◽  
pp. 370-388 ◽  
Author(s):  
J. Meinguet
Keyword(s):  
Error Bounds ◽  
Optimal Approximation

scholarly journals Approximate Diagonal Integral Representations and Eigenmeasures for Lipschitz Operators on Banach Spaces

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 220
Author(s):  
Ezgi Erdoğan ◽  
Enrique A. Sánchez Pérez
Keyword(s):  
Banach Spaces ◽  
Error Bounds ◽  
Stochastic Approach ◽  
Integral Representations ◽  
Spectral Theorem ◽  
Focus Attention ◽  
Normed Spaces ◽  
Whole Space ◽  
Convexity Properties ◽  
Lipschitz Operators

A new stochastic approach for the approximation of (nonlinear) Lipschitz operators in normed spaces by their eigenvectors is shown. Different ways of providing integral representations for these approximations are proposed, depending on the properties of the operators themselves whether they are locally constant, (almost) linear, or convex. We use the recently introduced notion of eigenmeasure and focus attention on procedures for extending a function for which the eigenvectors are known, to the whole space. We provide information on natural error bounds, thus giving some tools to measure to what extent the map can be considered diagonal with few errors. In particular, we show an approximate spectral theorem for Lipschitz operators that verify certain convexity properties.

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

Sign in / Sign up

Export Citation Format

Share Document