Specifically, suppose μ a measure on ( T, B ( T ) ) ( B ( T ) is the σ-algebra of Lebesgue measurable subsets of T) which is equivalent to the Lebesgue measure and verifies ∫ T r x ( t, t ) d μ ( t ) < ∞ (9).
On the other hand, the prevalence verified is equivalent to other studies if only considering clinical cases (6.9%).
Case 1. Then (3.36) is equivalent to (3.37). it is easy to verified.
In particular, since ℛ K) ≤ 0 is equivalent to T K) ≥ 0, Step 4 verifies that condition (b) of Claim 1 in Appendix 1 is satisfied.
Indeed, elimination lemma shows that existence of matrices X i = X i * > 0, F and A 0 verifying (15) is equivalent to existence of matrices X i = X i * > 0 and A 0 verifying the following two inequalities: I A i 0 r X i + r ̄ X ̄ i ′ r X i + r ̄ X ̄ i 0 1 A i ′ < 0, (19) I A 0 0 r X i + r ̄ X ̄ i ′ r X i + r ̄ X ̄ i 0 1 A 0 ′ < 0. (20..
It is not difficult to verify that this inequality is equivalent to 1 13 + 1 13 c 2 + 1 6 c ≤ c, which is satisfied if and only if 0.135 ≤ c ≤ 7.36.
It is easy to verify that problem (2.2) is equivalent to the following system of integral equations: x_{i}(t)=int_{t}^{1} varphi^{-1}biggl int_{0}^{s} F^{i}bigl(tau,x_{1}(tau),x_{2}(tau), ldots,x_{n}(tau)bigr), dtaubiggr), ds,quad i=1,2,ldots,n, where (tin[0,1]).
It is not difficult to verify that solving (2.1) is equivalent to the fixed point problem of finding x ˜ ∈ C such that x ˜ = P Fix ( T ) ∩ Fix ∩ Ξ S x ˜, where P Fix ( T ) ∩ Fix ∩ Ξ stands for the metric projection onto the closed convex set Fix ( T ) ∩ Fix ∩ Ξ. Problem (2.1) contains the hierarchical variational inequality problems considered and studied in [8, 18, 19] and the references therein.
The latter is based on Greenwood's estimate, which we empirically verified is equivalent to the Greenwood-type estimate of the variance for competing risks (Equation (6) in [ 13]).
It is easy to verify that the alternative process is equivalent to the previous one.
