Abstract
The paper deals with the operator of metric projection onto an arbitrary one-dimensional Chebyshev subspace 〈φ〉 of the space C[K] of real-valued functions defined and continuous on a Hausdorff compact set K. The linearity coefficient of the operator is calculated in terms of the parameters of the generating function φ. As a consequence, a new estimate of the Lipschitz constant of the operator is obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. A. Borodin, “The linearity coefficient of metric projections onto a Chebyshev subspace,” Mat. Zametki 85(2), 180–188 (2009) [Math. Notes 85 (2), 168–175 (2009)].
A. K. Cline, “Lipschitz conditions on uniform approximation operators,” J. Approx. Theory 8(2), 160–172 (1973).
A. Haar, “Die Minkowskische Geometrie und die Annäherung an stetige Funktionen,” Math. Ann. 78(1), 294–311 (1917).
P. S. Aleksandrov, Introduction to Set Theory and General Topology (Fizmatlit, Moscow, 2009) [in Russian].
V. I. Berdyshev, “Metric projection onto finite-dimensional subspaces from C and L,” Mat. Zametki 18(4), 473–488 (1975).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K. V. Chesnokova, 2014, published in Matematicheskie Zametki, 2014, Vol. 96, No. 4, pp. 588–595.
Rights and permissions
About this article
Cite this article
Chesnokova, K.V. The linearity coefficient of metric projections onto one-dimensional Chebyshev subspaces of the space C . Math Notes 96, 556–562 (2014). https://doi.org/10.1134/S0001434614090302
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434614090302