Zalizko V. Estimates coconvex approximation

The maine results of the thesis is the following: 1) it is proved that the classic Jeckson-Stechkin inequality connecting a value of the best uniforme approximation of any continious on the real axe periodic function by trigonometric polynomials with its k-th modules of continuity, is thrue for coconvexe approximation with k=3 as well; 2) it is proved that this ineguality is invalide for coconvex approximation with k>3; 3) it is proved that the clasic estimate of Nikolskii type of pointwise approximation by algebraic polynomyals on an interval holds for coconvex approximation if a function has more than one inflaction points and its smoothness is carecterized by third modulus of continuity; 4) the pointwiese estimates of coconvex approximation of functions from class W^r, r>3, with more them one inflaction points is obtained. The same problems are investigated for spline coconvex approximation as well.