When Z is a Hausdorff topological space, a multifunction G : Z → P f ( X ) is said to be h-continuous if it is continuous as a function from Z into ( P f ( X ), h ).
Let Z be a complete metric space, also (H: mathcal{X}rightarrow P_{f}(Z)) is called 'h-continuous' (resp. 'h-Lipschitz') if it is continuous (resp. Lipschitz) as a function from Z into (P_{f}(Z,d_{H})).
end{aligned} As ψ is continuous from the right and ({b_{n}}searrow L^), letting (nrightarrowinfty) we deduce that (lim_{nrightarrowinfty}varphi (b_{n})=0).
end{aligned} As F is continuous from the right, there exists a real number (h>1) such that Fbigl(hH(Tx_{0},Tx_{1} bigr)leq Fbigl(H(Tx_{0},Tx_{1}) bigr)+tau.
As is continuous, from a well known result in -fuzzy (probabilistic) normed space (see, [51, Chap.
On the other hand, for t ∈ I, as (s,ξ) → C(t - s)ξ is continuous from to X and is relatively compact, is relatively compact as well in X.
Typically, the CNTs in a VACNT array, if using a predeposited metal film as the catalysts, are continuous from the bottom to the top.
This region is now discontinuous, but the High Mountain Domain habitat was continuous from mountain to mountain as recently as the early Holocene.
Let be a semitopological semigroup, a nonempty subset of a Banach space then a representation of as mappings from into is continuous if defined by is continuous when has the product topology.
As f is continuous, we obtain from the dominated convergence theorem u (t) =int_{-infty}^{infty} G t,s) bigl[ fbigl s, u bigl s-alpha_{1}(s)bigl s-alpha_{bigl(s-alpha_{m}(s) bigr)bigr) bigr],ds.
Next, as is continuous and one-to-one, it follows from (c) that the sequence converges to.
