Sentence examples for by a suitable condition from inspiring English sources
In the following theorem, we replace the continuity of the operator T by a suitable condition.
Like in [13] we can replace the continuity of the operator T by a suitable condition.
The continuity of the mapping T can be replaced by a suitable condition (4′) (see Theorem 2.2 [13]): (4′) If { x n } is a sequence in X such that α ( x n, x n + 1 ) ≥ 1 for all n and x n → x ∈ X as n → ∞, then there exists a subsequence { x n ( k ) } of { x n } such that α ( x n ( k ), x ) ≥ 1 for all k.
The machine problem and its irregularity can be detected at an early stage by employing a suitable condition monitoring accompanied with powerful signal processing technique.
In the following theorem, we omit the p-continuity by replacing a suitable condition on the obtained iterative sequence.
x strictly on the boundary ∂D of a convex, bounded subset D ⊂ E (or, more practically, of the ball B ( 0, R ) ⊂ E ), condition (iigrowth) to be replaced by a suitable growth condition which would allow us reasonable applications (the usage of the Bernstein-Nagumo-Hartman-type condition will be employed in this context by ourselves elsewhere).
And then by adding a suitable regularity condition on a weight function, we derive and prove a cross-weighted norm inequalities between the Hardy-Littlewood maximal function and the sharp maximal function.
As shown from SEM micrographs in Figure 1, bead-free and continuous SF/CS NFs with different CS contents could be prepared by choosing a suitable electrospinning conditions.
We point out that an arcwise connected cone-quasiconvex set-valued mapping is characterized by a selection satisfying suitable conditions.
It is also possible that the mapping satisfies locally contractive conditions on a sequence contained in a closed ball in M. One can obtain fixed point results for such a mapping by using the suitable conditions.
Question Would Theorem 3.7 remain true if (i - v) i - veorem 3.7 were substinuTheoremsome suitable conditions?
