Sentence examples for proved ordered from inspiring English sources

Further, Harjani and Sadarangani [26] proved the ordered version of Theorem 1.2, Amini-Harandi and Emami [12] proved the ordered version of Rich type fixed point theorem, and Harjani and Sadarangani [27] proved ordered version of Theorem 1.3.

To command, punish, prove, order, point out, relate and predict are all variants of the word for "say .It's enough to make you tear your hair out.

Furthermore, we prove order-1 periodic solution is stable under certain conditions.

Recently, Harjani et al. [3] proved the ordered version of Theorem 1.

Fixed point and common fixed point results can be proved in ordered g.m.s., as well.

In this way, the results proved in ordered metric spaces are generalized (see for details [7] and the references therein).

Specifically, they proved that ordering and concatenation are together sufficient for the construction of an additive numerical representation of the relevant magnitudes.

In the recent years, a multitude of order-theoretic metrical fixed point theorems have been proved for order-preserving contractions.

In recent years, a multitude of order-theoretic metrical fixed point theorems have been proved for order-preserving contractions.

And then some coupled fixed point theorems were proved in partially ordered metric spaces.

Under German terrorism laws existing at the time of the attacks, specific knowledge of terrorist activity must be proved in order to convict a defendant of conspiracy.