Geodesic
A Chebyshev-Type Theorem Characterizing Best Approximation of a Continuous Function by Elements of the Sum of Two Algebras
Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 19-26.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, we consider the problem of uniform approximation of a continuous function defined on a compact metric space $X$ by elements of the sum of two algebras in the space of all continuous functions on $X$. We prove a Chebyshev-type theorem for characterization of best approximation.
Keywords: function algebra, best approximation, lightning bolt, extremal lightning bolt. 
@article{MZM_2021_109_1_a1,
     author = {A. Kh. Askarova and V. \`E. Ismailov},
     title = {A {Chebyshev-Type} {Theorem} {Characterizing} {Best} {Approximation} of a {Continuous} {Function} by {Elements} of the {Sum} of {Two} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {19--26},
     publisher = {mathdoc},
     volume = {109},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a1/}
}
TY  - JOUR
AU  - A. Kh. Askarova
AU  - V. È. Ismailov
TI  - A Chebyshev-Type Theorem Characterizing Best Approximation of a Continuous Function by Elements of the Sum of Two Algebras
JO  - Matematičeskie zametki
PY  - 2021
SP  - 19
EP  - 26
VL  - 109
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a1/
LA  - ru
ID  - MZM_2021_109_1_a1
ER  - 
%0 Journal Article
%A A. Kh. Askarova
%A V. È. Ismailov
%T A Chebyshev-Type Theorem Characterizing Best Approximation of a Continuous Function by Elements of the Sum of Two Algebras
%J Matematičeskie zametki
%D 2021
%P 19-26
%V 109
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a1/
%G ru
%F MZM_2021_109_1_a1
A. Kh. Askarova; V. È. Ismailov. A Chebyshev-Type Theorem Characterizing Best Approximation of a Continuous Function by Elements of the Sum of Two Algebras. Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 19-26. http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a1/

[1] I. P. Natanson, Konstruktivnaya teoriya funktsii, GITTL, M.–L., 1949 | MR | Zbl

[2] R. C. Buck, “Alternation theorems for functions of several variables”, J. Approx. Theory, 1 (1968), 325–334 | DOI | MR | Zbl

[3] B. Brosowski, A. R. da Silva, “A general alternation theorem”, Approximation Theory (Memphis, TN, 1991), Lecture Notes in Pure and Appl. Math., 138, Dekker, New York, 1992, 137–150 | MR

[4] A. Kh. Asgarova, V. E. Ismailov, “Diliberto-Straus algorithm for the uniform approximation by a sum of two algebras”, Proc. Indian Acad. Sci. Math. Sci., 127:2 (2017), 361–374 | DOI | MR | Zbl

[5] A. Kh. Asgarova, V. E. Ismailov, “On the representation by sums of algebras of continuous functions”, C. R. Math. Acad. Sci. Paris, 355:9 (2017), 949–955 | DOI | MR | Zbl

[6] D. E. Marshall, A. G. O'Farrell, “Uniform approximation by real functions”, Fund. Math., 104:3 (1979), 203–211 | DOI | MR | Zbl

[7] D. E. Marshall, A. G. O'Farrell, “Approximation by a sum of two algebras. The lightning bolt principle”, J. Funct. Anal., 52:3 (1983), 353–368 | DOI | MR | Zbl

[8] Yu. P. Ofman, “O nailuchshem priblizhenii funktsii dvukh peremennykh funktsiyami vida $\varphi(x)+\psi(y)$”, Izv. AN SSSR. Ser. matem., 25:2 (1961), 239–252 | MR | Zbl

[9] V. E. Ismailov, “Characterization of an extremal sum of ridge functions”, J. Comput. Appl. Math., 205:1 (2007), 105–115 | DOI | MR | Zbl

[10] V. E. Ismailov, “On the approximation by compositions of fixed multivariate functions with univariate functions”, Studia Math., 183:2 (2007), 117–126 | DOI | MR | Zbl

[11] W. Rudin, Functional Analysis, McGraw-Hill, New York, 1991 | MR | Zbl

[12] S. Ya. Khavinson, “Chebyshevskaya teorema dlya priblizheniya funktsii dvukh peremennykh summami $\varphi(x)+\psi(y)$”, Izv. AN SSSR. Ser. matem., 33:3 (1969), 650–666 | MR | Zbl