For each real number h n with 0 < h n < 1 and h n → 1 as n → ∞, we define T n : M → K ( M ) b y T n x = h n T x + ( 1 - h n ) q. Obviously each T n is f-contraction map.
Obviously, △ n ( t ) ≤ t for any n ∈ N and t ∈ [ 0, 1 ].
Obviously, when D n (t) = 0, M n (t) may take the maximum value M n which can be expressed as M n = E n init - τ n P n sens t - E th r P n elec + P n tran KL, ∀ n ∈ 1, 2, …, N. (56).
Obviously, T n λ 1 and T n λ 2 contain only two Fatou periodic domains A λ ( 1 ) and A λ.
We define the operator N Γ Γ → W 1, 2, N ( x ) = L − 1 ( f − A ( t, x ) ). Obviously, N is compact.
From the asymptotic BER obtained for N t =2, MRT obviously outperforms EGT because of the weighting factor of the 1/ρ2 term, i.e., 3/16 instead of 1/4.
Obviously, the Eq. 7 solution depends on n(t)/n(0) function.
Obviously, x ( t ) = ∑ n = 0 ∞ x n ( t ) is a continuous solution of (2.2).
Obviously, t N ∩ C N ( b ) = ∅ and ( C N ( t ) ∩ C N ( b ) ) p ′ = Z ( N ) p ′, this shows that the group ( C N ( b ) / Z ( N ) ) p ′ acts on the set { t N } fixed-point-freely.
Obviously, T is an asymptotically nonexpansive mapping with Lipschitz constants l n ( T ) = ( 1 + 1 n ln 2 n ).
Obviously, to obtain the energy availability of the n th relay node, D n (t) should be measured firstly.
