On the best approximation and exact evaluation of the widths of some classes of functions in the Bergman space Bp, 1≤p≤∞

The width of various classes of functions in the Hardy space, which are defined by the moduli of continuity and smoothness, are evaluated. The best approximation to the function are estimated by using the triangle inequality and the result is obtained by applying Minikowski inequality after simple algebraic calculation. The second term is estimated with r=2 and is integrated twice by parts. To derive a lower bound for the Bernstein width, the (n+1)-dimensional ball of polynomials are considered. Several theorems are solved using the Bernstein width and applying Tikhomirov's theorem. The exact value of the width for corresponding classes of functions can be obtained by applying the theorem.