Table 8 The hypotheses results Not satisfied Partial satisfied Satisfied Basic model Hypothesis 1 X Hypothesis 2 X Hypothesis 3 X Sensitivity analysis Hypothesis 1 X Hypothesis 2 X Hypothesis 3 X.
From now on we shall assume that the following hypothesis is satisfied [cf. Theorem 3.1 iii)].
Definition 2.1 We say that Problem (5) is Banach admissible if the following hypothesis is satisfied: max 1 ≤ i ≤ m max 1 ≤ j ≤ m { | α i j | k i j ∕ r i } < 1.
The result shows that the larger the sampling size (at least larger than the size of the shrub component), the better the hypothesis is satisfied because of the unique structure of the Jornada scene: dense plant clumps (shrub component) sparsely scattered on a predominantly bare soil background.
Throughout this paper, we suppose that the following hypothesis is satisfied: ((A_{1})): (f in C [ {0, + infty} ) timesmathbb{R}^{3} tomathbb {R}) is an (L^{1} -Caratheodory function, that is, f is a Caratheodory function, and for any (r > 0), there exists a nonnegative function ({g_{r}}(t) in{L^{1} -Caratheodory such that biglvert {functionw)} bigrverthat{g_{r}}(t),quad mbox{a.e.
Suppose that the following hypotheses are satisfied: (i).
A nonempty, closed set is said to be a cone provided that the following hypotheses are satisfied: (1) if,, then (2) if,, then .
Also, assume that the following hypotheses are satisfied: (a) F ( X × X ) ⊂ X ; (b) if G X × X → R, G G ( x, y ) = q ( F ( x, y ), x ), then for each sequence ( x n, y n ) → ( u, v ), we have G ( u, v ) ≤ k lim inf n → ∞ G ( x n, y n ) for some k > 0. .
Suppose that the following hypotheses are satisfied: (i) If (x n ) is a nonincreasing sequence in X with respect to ≼ such that x n → x ∈ X as n → +∞, then x n ≽ x for all n ∈ ℕ. (ii) f(fx) ≼ fx for all x ∈ X. .
A nonempty closed set (Psubset E) is said to be a cone provided the following hypotheses are satisfied: (i) if (uin P), (lambdageq0), then (lambda u in P); (ii) if (uin P) and (-uin P), then (u=0). . if (uin P), (lambdageq0), then (lambda u in P); if (uin P) and (-uin P), then (u=0).
