Some uniform approximation theorems of yk-analytical functions

The paper examines some issues of uniform approximation of y^k -analytical functions infinite simply connected regions in the upper halfplane y >0 whose boundary includes a section of the real axis. Polozhii's integral representation of y^k -analytical functions [3] makes it possible to extend a number of theorems of uniform approximation of analytical functions by polynomials to the class of y^k-analytical functions.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 57, pp. 3–12, 1985.