Sentence examples for order divided from inspiring English sources

The r-convex function is characterized by the rth order divided difference as follows (see [2], p.14).

The following definition of a real valued convex function is characterized by second order divided difference (see [[1], p.15]).

The mean stream lengths were calculated using the formula of total stream length of order divided by total number of stream segments of order.

holds for every α, β ∈ ℝ and x, y ∈ I. Definition 2. The second order divided difference of a function f : [a, b] → ℝ at mutually different points y0, y1, y2 ∈ [a, b] is defined recursively by (18).

To avoid the computation of F ″ ( x n ), and to maintain the high order convergence, many researchers have replaced the second order derivative with the first order divided differences.

In the paper [24] Daletskii and Krein proved that in the case when the self-adjoint operator A is bounded for nice functions f the map (tmapsto f(A+tK)) has m-th derivative and it can be expressed in terms a multiple operator integral whose integrand is a higher order divided difference of f.

Even his willingness to use executive orders divided the crowd into partisan camps.

A th-order divided difference of at distinct points is defined recursively by (51).

First, note that function defined in (5.8) is the 1st-order divided difference of function.

Recall that a function is 3-convex if for, and, where denotes third-order divided difference of.

In this article, we give more generalized results than in Anwar et al. (2010) and Latif and Pečarić (2010) in new direction by using second-order divided difference.