Obviously,,, are nondecreasing in the first variable, while decreasing in the second variable.
Remark 7. If we take Ω = ℕ0 × ℕ0, w(m, n) ≡ 0, α(m) = m, β(n) = n, and omit the conditions "w is nondecreasing in the first variable, while decreasing in the second variable", " is nondecreasing in the first variable and decreasing in the second variable", and "b is decreasing in the second variable" in Theorem 2.8, then Theorem 2.8 reduces to [[13], Theorem 5].
Suppose u, a, b, f, g, h, w ∈ ℘+, and b, f, g, h, w are nondecreasing in the first variable, while decreasing in the second variable.
provided that, and is nondecreasing in the first variable and decreasing in the second variable, where K > 0 is a constant, and (21).
Remark 4. If we take Ω = ℕ0 × ℕ0, w(m, n) ≡ 0, α(m) = m, β(n) = n, and omit the conditions "f, g, h, w are nondecreasing in the first variable, while decreasing in the second variable" and "b is decreasing in the second variable" in Theorem 2.5, then Theorem 2.5 reduces to [[14], Theorem 7].
where u, a, b, f, g, h, w ∈ ℘+ with a(m, n) not equivalent to zero, and f, g, h, w are nondecreasing in the first variable, while decreasing in the second variable, a is nondecreasing in the first variable, and b is decreasing in the second variable, α, β, p, q, r, l are defined as in Theorem 2.1.
Assume that a(m, n) is decreasing in the first variable.
If. for (m, n) ∈ Ω, then (2) Assume that a(m, n) is decreasing in the first variable.
Suppose u, a, b, f, g, h, w ∈ ℘+, and b, f, g, h, w are decreasing in the first variable, while nondecreasing in the second variable.
We unexpectedly found fecundability increasing rather than decreasing in the first menstrual cycles.
Real disposable personal income actually decreased in the second and third quarters of 2011 and was essentially unchanged for the year.
