Approximation Characteristic Of The General Sobolev Space With Probabilistic Case Setting And Average Case Setting

In the present article,we investigate some approximation characteristic of the general Soblove with mixed derivative W₂r (T) in the Probabilistic Case Setting and Average Case Setting.We present sharp bounds on the Kolmogorov (N ,δ)-widths,p-average Kolmogorove N -widths,linear probabilistic(N,δ)-widths,p-average linear N -widths of W₂r (T) in the space S_q(T),that is Where Sq (T) is a subspace of L₁ (T),in which the Fourier series is absolutely convergent in l_q sense, 0 <δ≤12 andρ>1 depends only on the eigenvalues of the correlation operator of the measureμ.