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Keywords: approximation theory, Chebyshev set, metric projection.

### Research interests:

→ Approximation theory and Geometry of Banach spaces.

→ Density of a semigroup in a Banach spaces.

### Publications:

*2024*

→ K. S. Shklyaev, "On Locally Chebyshev Sets", Math. Notes, 115:4 (2024), 636–641, DOI.

*2023*

→ K. Shklyaev, "Approximation by sums of shifts and dilations of a single function and neural networks", Journal of Approximation Theory, 291 (2023), 105915, DOI.

→ P. A. Borodin, K. S. Shklyaev, "Density of quantized approximations", Uspekhi Mat. Nauk, 78:5(473) (2023), 3–64, DOI.

*2022*

→ K. S. Shklyaev, "The convex hull and the Carathéodory number of a set in terms of metric projection", Mat. Sb., 213:10 (2022), 167–184, DOI.

→ K. S. Shklyaev, "Density of the Semigroup Generated by Curves through Zero in a Banach Space", Math. Notes, 111:2 (2022), 324–328, DOI.

*2021*

→ K. S. Shklyaev, "Plane sets being Chebyshev in some norm", Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2 (2021), 35–39.

→ P. A. Borodin, K. S. Shklyaev, "Approximation by simple partial fractions in unbounded domains", Sb. Math., 212:4 (2021), 449–474, DOI.

*2020*

→ K. S. Shklyaev, "A connected compact locally Chebyshev set in a finite-dimensional space is a Chebyshev set", Sb. Math., 211:3 (2020), 455–465, DOI.

*2017*

→ K. S. Shklyaev, "Metric projection onto subsets of compact connected two-dimensional Riemannian manifolds", Moscow University Mathematics Bulletin, 72:4 (2017), 149–153, PDF.