The topographical data with U = 0, and F > 0 (free-face is available) is satisfying this condition.
Under suitable assumptions, we prove that any solution of the above inequality has to be uniformly close to an orthogonally additive mapping, that is, satisfying the condition.
Corollary 2.11 Let ( X, ϑ ) be a S-complete Hausdorff uniform space such that p is an E-distance on X. Suppose that a mapping T : X → X is satisfying the condition α ( x, y ) max { p ( T x, y ), p ( x, T y ) } ≤ ψ ( p ( x, y ) ), for any x, y ∈ X, where ψ ∈ Ψ.
To obtain the relationship between the slope angle factor S and the upslope factor U, a comparison between shallow landslides and stable slopes is needed with the same value of the cross-section factor C and free-face factor F. The topographic data in which C = 0, and F > 0 (free-face is available) is satisfying this condition.
All we're focused on is satisfying those conditions," Jim Leech, chief executive officer at the pension plan, told The Globe and Mail.
Then in all the above cases, the mappings f, g, h, R, T, and S are satisfying the condition (2.1) of Theorem 2.1 with k = 1 4, so that all the conditions of Theorem 2.1 are satisfied.
Then in all the above cases, the mappings S, T, R, A, B, and C are satisfying the condition (2.17) of Theorem 2.3 with k = 2 21.
Now we prove that the mappings f, g, h, R, S, and T are satisfying the condition (2.1) of Theorem 2.1 with k = 1 4 ∈ [ 0, 1 ).
We note that Bennett only proved Theorem 1.1 for p, q, r ≥ 1 but as was pointed out in [3], Bennett's proof actually works for the p, q, r's satisfying the condition in Theorem 1.1.
Our choice of metals for the electrical contacts therefore appears to be satisfying these conditions.
