Sentence examples for is only continuous from inspiring English sources

The latter result fails if is only continuous.

Indeed, the quasi-nonexpansive mapping is only continuous in its fixed point set.

In Section 3, we establish the existence of mild solutions of (1.1) when the nonlocal item is only continuous.

In this section, by using the techniques of approximate solutions, analytic resolvent and fixed point, we prove an existence theorem for the nonlocal problem (1.1) when the nonlocal item g is only continuous in C ( [ 0, b ], X ).

The number ({2q/ q-2)}:= 2^{sharp}) is the critical Sobolev exponent, since for a bounded domain Ω and (2 < p < {2q/ q-2)}), the (S_{0}^{1,2}(Omega)) is compactly embedded into (L^{p}(Omega)), while this inclusion is only continuous if (p = 2q/ q-2)).

We construct a new homotopy operator and then weaken the assumption that f is (C^{1}) to that of f being only continuous.

Using the techniques of approximate solutions and fixed point, existence results are obtained, for mild solutions, when the impulsive functions are only continuous and the nonlocal item is Lipschitz in the space of piecewise continuous functions, is not Lipschitz and not compact, is continuous in the space of Bochner integrable functions, respectively.

Note, however, that the coefficients of η in this construction are only continuous in the variable w and so the Cauchy Fantappié form Ω 0 cannot be defined for such η because doing so would require differentiating the coefficients of η with respect to w, see (4.4).

It is only the continuous renewal of his vision – either in the form of evolution or of rediscovery – that can keep his music-making young".

If h is only a continuous surjection then we have a semiconjugacy.

We make use of this transformation because beyond the edge of the front of infected cells and viruses, there is only a continuous medium of tumor cells.