No abstract

Abstract. Firstly, we introduce a new type of weight functions named as N-doubling weights, which is an essential generalization of the well known doubling weights. Secondly, we establish a weighted Turán type inequality with N-doubling weights and a Nikolskii-Turán type inequality for rational functions with prescribed poles. Our results generalize some known Turán type inequality both for polynomials and rational functions.Mathematics subject classification (2010): 41A17, 26D10.

Let {λ n } be a sequence of real numbers, satisfying 0 λ 1 < λ 2 < • • • , and λ n+1 − λ n Mn with M a positive constant. This note gives a Jackson type theorem for Müntz rational approximation in L p spaces by using a new kind of Ditzian-Totik type modulus.

Abstract. We prove that, for a sequence of positive numbers δ(n), if n

Abstract. In this paper, we will generalize the result in weighted integrability to include all positive non-integers γ connecting with derivatives of the sum-functions.Mathematics subject classification (2010): 42A25, 42A50.