By the hypothesis, f is continuous in S ⊂ D1 uniformly for t ∈ T ; so is φ.
By hypothesis, T is continuous in ( X 2, d 2 ), and hence by (2.5) it follows that Z ¯ is a fixed point of T, that is, T ( Z ¯ ) = Z ¯.
Throughout this paper, we always assume that, and nonlinear term satisfies the following hypothesis: (H) is continuous, nondecreasing on and nonincreasing on for each fixed, and there exists a real number such that, for any, (1.2). there exists a function, and is integrable on such that (1.3).
For the function, we impose the following hypotheses: (H1) is continuous; (H2 for fixed, is monotone increasing on ; (H3 there exists such that (13).
Suppose that satisfies the following hypotheses: (H) is continuous on and the limits, exist and are finite for and. . is continuous on and the limits, exist and are finite for and.
Let F : X n → X be a given mapping satisfying the following hypotheses: (1) F is continuous, (2) F has the mixed strict monotone property, (3) for all ϵ > 0, there exists δ > 0 such that ϵ ≤ ∫ 0 max { p ( x 1, y 1 ), p ( x 2, y 2 ), …, p ( x n, y n ) } φ ( t ) d t < ϵ + δ ⇒ ∫ 0 p ( F ( x 1, …, x n ), F ( y 1, …, y n ) ) φ ( t ) d t < ϵ .
Our hypothesis is that continuous characterization of traffic, local meteorology, and other statistical parameters will allow for quantification and characterization of distance-dependent relationships relative to background concentrations for mobile-monitored concentrations of UFPs and PM2.5.
Our hypothesis is that continuous infusion of local anaesthetic following rotator cuff surgery would be equivalent to pain relief provided by a placebo in the setting of pre-emptive ropivacaine, intra-operative parecoxib and post-operative intravenous morphine and oral dextropropoxyphene hydrochloride/paracetamol available on demand.
By our hypothesis, we know that is continuous.
