No abstract

Abstract. The weighted approximation errors of Baskakov operator is characterized for weights of the form w(x) = x γ 0 (1 + x) γ∞ , where γ 0 ∈ [−1,0] , γ ∞ ∈ R . Direct inequalities and strong converse inequalities of type A are proved in terms of the weighted K -functional.Mathematics subject classification (2010): 41A36, 41A25, 41A27, 41A17.

We study the behavior of the smallest possible constants d(a, b) and dn in Hardy's inequalities b a 1 x x a f (t)dt 2 dx ≤ d(a, b) b a f 2 (x)dx and n k=1 1 k k j=1 a j 2 ≤ dn n k=1 a 2 k .The exact constant d(a, b) and the exact rate of convergence of dn are established and the extremal function and the "almost extremal" sequence are found.

No abstract

No abstract