Sentence examples for mutually different points from inspiring English sources

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).

Let Ω = {f s : s ∈ I} be a family of functions defined on [a, b] such that the function s ↦ [y0, y1, y2; f s ] is exponentially convex on I for every three mutually different points y0, y1, y2 ∈ [a, b].

Let (Lambda={ f_{p}: pin J }), where J is an interval in (mathbb{R}), be a family of functions defined on an interval I in (mathbb{R}) such that the function (p mapsto[x_{0},ldots,x_{n};f_{p}]) is k-exponentially convex in the Jensen sense on J for every ((n+1)) mutually different points (x_{0},dots,x_{n}in I).

Let (Lambda={f_{p}:pin J}), where J is an interval in (mathbb{R}), be a family of functions defined on an interval I in R such that the function (pmapsto [x_{0},dots,x_{n};f_{p}]) is exponentially convex in the Jensen sense on J for every ((n+1)) mutually different points (x_{0},dots,x_{n}in I).

Let ϒ = {f s : s ∈ I} be a family of functions defined on [a, b] such that the function s ↦ [y0, y1, y2; f s ] is log-convex in J-sense on I for every three mutually different points y0, y1, y2 ∈ [a, b].

Let (Lambda={f_{p}:pin J}), where J is an interval in (mathbb{R}), be a family of functions defined on an interval I in (mathbb{R}) such that the function (pmapsto[x_{0},dots,x_{n};f_{p}]) is 2-exponentially convex in the Jensen sense on J for every ((n+1)) mutually different points (x_{0},dots,x_{n}in I).

Zeros of (p_{4}) are mutually different and different from 1.

In regions A and B the coefficient remains constant but mutually different.

If (0ne bdne-4a^{3}/27 bdne-4a^{3}/27os of (108) are muthenly differenthe

Both candidates had different points of emphasis.

Old editions have different points.