Sentence examples for on a bounded interval from inspiring English sources

The following Scorza-Dragoni theorem explains the structure of the Carathéodory functions on a bounded interval.

In [3], the author studied a similar problem posed on a bounded interval.

We notice that all the papers mentioned above were investigated mild solutions on a bounded interval.

Later, Dobrescu and Matei [9] discussed the approximation of B-continuous functions on a bounded interval by a generalized Boolean sum of bivariate generalization of Bernstein polynomials.

The fractional Laplacian operator on a bounded interval is defined in terms of the eigenvalues and eigenfunctions of the Laplacian operator [8, 11].

First, we consider problem (1.1 - 1.2) on a bounded interval, and then we let the interval go to infinity to get hyperbolic orbits.

Let { X ( t ) } t ≥ 0 be an R d -value martingale and let [ a, b ] be a bounded interval on R +.

Let Γ and Λ denote the following classes of functions: (Gamma={etacolon[0, infty) longrightarrow[0, infty), eta mbox{ is continuous and monotonic increasing}}); (Lambda={xicolon[0, infty) longrightarrow[0, infty), xi mbox{ is bounded on any bounded interval in } [0, infty)}).

If β ≥ 1, then it is easily seen that f satisfies the Lipschitz condition with respect to x on any bounded interval.

By the Ascoli-Arzela theorem, there exists a subsequence of { t n }, we still denote it as { t n }, such that x ( t + t n ) → p ( t ), y ( t + t n ) → q ( t ), as n → + ∞ uniformly in t on any bounded interval in.

Let and be two twice continuously differentiable convex functions defined on a closed bounded interval and let the weight function be equal to (2.17).