Let ω : [ 0, γ ) → R + be a non-increasing and locally integrable function called a weight function. Let us define γ 0 = sup { t ≥ 0 : ω is constant on ( 0, t ) }, α = sup { t ≥ 0 : ω ( t ) > 0 }. We say that a weight function ω is regular if there exists η > 0 such that ∫ 0 2 t ω ( t ) d t ≥ ( 1 + η ) ∫ 0 t ω ( t ) d t. for any t ∈ [ 0, γ / 2 ) (see [22 25]).
From [1] or [3] a E-J generalized Hausdorff matrix (for ) is regular if and only if there exists a function with such that (12). in which case is called the moment generating function, or mass function, for and is called moment sequence.
And ( X, d, ≼ ) is regular if it is both nondecreasing-regular and nonincreasing-regular.
Let T : X k → X k be an isotone mapping for which there exists a constant α ∈ [ 0, 1 ) such that, for all Y, V ∈ X k with Y ≥ V, ρ k ( T ( Y ), T ( V ) ) ≤ α ρ k ( Y, V ), (3.16). where ρ k is defined by (2.2). Suppose either T is continuous or ( X, ≤, d ) is regular. If there exists Z 0 ∈ X k such that Z 0 ≍ T Z Z 0 ), then T has a fixed point.
for some function ϕ ( z ) ∈ Ω and every z ∈ D. Next, let s 1 ( z ) = z + c 2 z 2 + c 3 z 3 + ⋯ and s 2 ( z ) = z + d 2 z 2 + d 3 z 3 + ⋯ be regular functions in D, if there exists ϕ ( z ) ∈ Ω such that s 1 ( z ) = s 2 ( ϕ ( z ) ) for all z ∈ D, then we say that s 1 ( z ) is subordinated to s 2 ( z ) and we write s 1 ( z ) ≺ s 2 ( z ), then s 1 ( D ) ⊂ s 2 ( D ).
But would there be regular everyday death even if everything was already dead?
"Should there be regular mental health exams?
"If an individual is shown to have that predisposition, then, for instance, there can be regular, closer monitoring".
There will be regular bus service citywide.
