It is shown that if ℓϕ is an Orlicz sequence space, then the space ℓw1 of weakly summable sequences in ℓϕ is continuously embedded into ℓϕ ℓ2) (resp., into ℓϕ whenever t↦ϕ is equivalent to a concave function (resp., a convex function and ϕ is a supermultiplicative function).
First, it is equivalent to the linear-discontinuous (LD) Galerkin method whenever that method yields a strictly non-negative solution.
A real function f is continuous if and only if ( f ( x n ) ) is a convergent sequence whenever ( x n ) is. Regardless of limit, this is equivalent to the statement that ( f ( x n ) ) is Cauchy whenever ( x n ) is.
Whenever (Aequiv0), problem (2.3) is equivalent to finding (uin C) such that F u, y geq0, quad forall yin C, (2.4) which is called the equilibrium problem.
Whenever (Fequiv0), problem (1.1) is equivalent to finding (uin C) such that langle Au,y-u ranglegeq0,quad forall yin C, which is called the variational inequality of Browder type.
ILS is equivalent to 'deep coalescence', which occurs with high probability whenever the time between speciation events is short relative to the population size (Maddison, 1997).
Whenever (Fequiv0), (Aequiv0), problem (2.3) is equivalent to finding (uin C) such that varphi y) geqvarphi u), quad forall yin C, which is called the convex optimization problem.
If, for example, ( a_1>0, a_2>0), then u blows-up whenever (p+ a_1q/a_2 >1); this inequality is equivalent to the condition (-rq + p-1)(s-1)>0), which is satisfied in this case (since (p<1+ p-1s< 1+q)).
Whenever (Aequiv0), (varphi(x equiv0), problem (2.3) is equivalent to finding (uin C) such that F u, y geq0, quad forall yin C, (2.4) which is called the equilibrium problem.
Whenever (Fequiv0), (varphi(x equiv0), problem (2.3) is equivalent to finding (uin C) such that langle Au,y-u ranglegeq0,quad forall yin C, which is called the variational inequality of Browder type.
