Let f(n) be a nonnegative function,and k,b,s_i and t_i(i=1,2,…) positive constants. We discuss the lower bound of rational approximations to two kinds of continued fractions such as [a_0,a_1,a_2,…]=[kn+b]_n~∞=0 and [s_n,f(n),t_n]_n~∞=1.
Let Tnf,a be the Toeplitz operator on A2,a(Bn), the main results of this paper include several characterizations for the compactness of there Toeplitz operators with a nonnegative symbol in L1,a(Bn). In particular, we show that the compactness of Tfn,σis actually independent of a when f is a nonnegative function in L1,a(Bn).
How to judge the divergence and convergence of the generalized integral ∫~(+∞)-af(x)dx is discussed through finding the related limit of non-negative function,and a method of judging the divergence and convergence of the flaw integral of a nonnegative function is given.
In this paper, we discuss the existence and nonexistence of solutions for the problem N > 4, where Ω is a bounded smoothness domain in R~N, λ∈ R~1 ,μ≥0 ,f(x) is a given nonnegative function. Some interesting results have been obtained.
The nonnegative function which measures the degree of degeneracy of ellipticity bounds is assumed to be exponentially integrable.
Let a(x) be a nonnegative function regularly varying at infinity with index greater than -1.
Given a metric space with a Borel measure, we consider the classes of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function summable with some power.
Given a metric space with a Borel measure μ, we consider a class of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function p-summable with respect to μ.
We call a nonnegative function ω Θ-admissible if in the space KΘ there exists a nonzero function f ∈ KΘ such that |f| ≤ ω a.e.
In the paper, two forms of kolmogorov's sufficient conditions for the continuity of a separable random process are discussed, and it is proved that the class of nonnegative monotonically nondecreasing functions in Kconditions can be replaced by a class of nonnegative functions. The structure of certain sufficient conditions is discussed. These results show that improved conditions are valid and efficient.
This paper investigates equation ( 1 ) in two cases :(i)P=0, (ii) P≠0 satisfies |P(t,x,y,z,w)|≤(A+ |y|+|z|+|w|)q(t), where q(t) is a nonnegative function of t. For case (i)the asymptotic stability in the large of the trivial solution x=0 is investigated and for case (ii) the boundedness result is obtained for solutions of equation ( 1 ). These results improve and include several well-known results.