Sentence examples for be an arbitrary fixed from inspiring English sources

In the rest of this subsection, let k 2 ′ be an arbitrary fixed number in { 1, …, K 0 − 1 }, and let D 2 ⊂ ⊂ Ω be an arbitrary fixed subdomain satisfying D 2 ∩ Γ k 2 ′ ∗ ≠ ∅, D ¯ 2 ∩ ( Γ k 2 ′ − 1 ∗ ∪ Γ k 2 ′ + 1 ∗ ) = ∅ and D ¯ 2 ∩ Γ ∗ ∗ = ∅.

Let (k_{0} in K) be an arbitrary fixed index and (V_{k_{0}}) be any (g -preopen set of (Y_{k_{0}}).

Let j be an arbitrary fixed integer.

Let (delta _{0}>0) be an arbitrary fixed real number.

Let (iota>0) be an arbitrary fixed number.

Let η be an arbitrary fixed point of Ω.

Let be an arbitrary but fixed.

Let n ∈ N be an arbitrary but fixed.

we shall show that ( x n ) n ∈ N possesses a convergent subsequence in L 1. Since P is weakly compact, for an arbitrary fixed ε > 0, by Theorem 2.5 there exists T > 0 such that ∫ T ∞ | x m ( t ) − x n ( t ) | d t ≤ ε 2 (4.7).

To begin, let T be an arbitrary threshold and fix γ at the desired GWER.

where is an arbitrary (but fixed) element in, and and are two sequences in It is proved, under certain appropriate assumptions on the sequences and that defined by (1.3) converges to a fixed point of (see [7]).