Book reviews: “Alexey R. Alimov and Igor’ G. Tsar’kov, Geometric approximation theory,” Springer Monographs in Mathematics. Cham: Springer 2022, xxi+508 p. ISBN: 978-3-030-90950-5/hbk; 978-3-030-90953-6/pbk; 978-3-030-90951-2/ebook).

Abstract

The origins of abstract approximation theory can be traced back to the years 50s of the 19th century when P.L. Chebyshev considered the problem of uniform approximation of continuous functions by polynomials in connection with some technical problems (the construction of some mechanisms as ”parallelograms” which transform a circular motion into a rectilinear one, devices used for steam engines). This proves that approximation theory had, and still have, important applications in various scientific and technical domains. Since then the domain developed in many directions by the contributions of many mathematicians and applied scientists.