Sentence examples for more general theorem from inspiring English sources

Both results are obtained as a consequence of a more general theorem concerned with continuous operator cocycles defined over a compact dynamical system.

There is a more general theorem concerning mixed strategy equilibrium.

A more general theorem should always precede a less general and more particular one.

We omit the details since a more general theorem is proved below.

Theorem 1.3 is established in Section 3 by proving a more general theorem.

Indeed, Theorem 2.5 is a special case of a more general theorem on majorization and convex functions.

In this paper, motivated by the above work, we will prove more general theorems and establish some new integral inequalities.

The above problem was solved by Bennett [2], who proved the following more general result: Theorem 1.1 ([2, Theorem 4]).

Remark 1 Theorem 2 is more general than Theorem 1 (i.e., Theorem 2.1 in [22]), since the contractive condition (2.1) is weaker than (1.6), a fact which is clearly illustrated by Example 1. Apart from these improvements, we note that our proof is significantly simpler and shorter than the one in [22].

It is also worth remarking that in his work [39], Ohsawa proved a much more general extension theorem that includes Theorem 5.8, and has a number of applications.

Hence, we find that our theorem is more general than Theorem 1.1 (Abkar and Gabeleh [13]).