Sentence examples for convergent decreasing sequence from inspiring English sources

We have introduced an algorithm to construct a convergent increasing sequence of lower solutions as well as a convergent decreasing sequence of upper solutions.

(b) Every bounded decreasing sequence in Y is convergent.  .

Every bounded decreasing sequence in Y is convergent.

Using inequalities (2.1) and (2.2), we deduce that { d ( f n x, f n + 1 x ) } is a decreasing sequence and hence it is convergent.

Definition 6 A cone K ⊂ E is called regular if every decreasing sequence of elements in K is convergent.

The cone is regular if every decreasing sequence which is bounded from below is convergent.

(iii) The cone is regular if every decreasing sequence which is bounded from below is convergent.  .

Equivalently, the cone (P) is regular if and only if every decreasing sequence which is bounded from below is convergent.

Equivalently, the cone is regular if and only if every decreasing sequence which is bounded from below is convergent [1].

Equivalently the cone is called regular if every decreasing sequence which is bounded from below is convergent.

So, the sequence ({S x_{n},x_{n},x_{n+1})}) is a decreasing sequence in (mathbb{R}^) and thus it is convergent to (tinmathbb{R}^).