Exact Solutions of Some Extremal Problems of Approximation Theory

2011 ◽  
pp. 221-229
Author(s):  
A. L. Lukashov
Keyword(s):  
Exact Solutions ◽  
Approximation Theory ◽  
Extremal Problems

Extremal problems of approximation theory in fuzzy context

1999 ◽  
Vol 105 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Svetlana V. Asmuss ◽  
Alexander P. Šostak
Keyword(s):  
Approximation Theory ◽  
Extremal Problems

scholarly journals On extremal problems of approximation theory for classes of functions of two discrete variables in $l^2_{q,p}$

2021 ◽  
Vol 15 ◽  
pp. 60
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Approximation Theory ◽  
Extremal Problems ◽  
Discrete Variables ◽  
Periodic Functions

For classes of $2\pi$-periodic functions of two discrete variables, defined on grid set $\sigma_{q,p}$, we found exact values of Kolmogorov and linear quasiwidths of classes $W^{r,p}(l^2_{q,p})$ in $l^2_{q,p}$ space.

Extremal Problems of Approximation Theory

2004 ◽  
pp. 201-254
Author(s):  
Roald M. Trigub ◽  
Eduard S. Bellinsky
Keyword(s):  
Approximation Theory ◽  
Extremal Problems

scholarly journals On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2200
Author(s):  
Anna Bahyrycz ◽  
Janusz Brzdęk ◽  
El-sayed El-hady ◽  
Zbigniew Leśniak
Keyword(s):  
Exact Solutions ◽  
Approximation Theory ◽  
Functional Equations ◽  
Approximate Solutions ◽  
Main Issue ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Stability Of Functional Equations

The theory of Ulam stability was initiated by a problem raised in 1940 by S. Ulam and concerning approximate solutions to the equation of homomorphism in groups. It is somehow connected to various other areas of investigation such as, e.g., optimization and approximation theory. Its main issue is the error that we make when replacing functions satisfying the equation approximately with exact solutions of the equation. This article is a survey of the published so far results on Ulam stability for functional equations in 2-normed spaces. We present and discuss them, pointing to the various pitfalls they contain and showing possible simple generalizations. In this way, in particular, we demonstrate that the easily noticeable symmetry between them and the analogous results obtained for the classical metric or normed spaces is in fact only apparent.

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