Sentence examples for main theorems due from inspiring English sources

We define the following iterative schemes for our main theorems due to the well-known Picard, Mann, Ishikawa iteration processes.

Our results contain properly the main theorem due to Suzuki [24] and many of its extensions [23] (see also [28]).

The main tool of our study are fixed point theorems due to Dhage for single-valued [27] and multi-valued [28] maps.

However, our main result given in Theorem 2.1 is not a consequence of any existing theorems due to the fact that the contraction condition contains the term d ( A, B ).

Now we shall prove our main theorems.

We now formulate our main theorems.

3, the main theorems are presented.

Now we present the main theorems.

Now, we will show our main theorems.

The main theorems are as follows.

By the main theorem on monotone operators due to Browder and Minty in [12], Theorem 26.A, the inverse operator (T :=F^{-1} colon X to X^) is bounded, continuous and satisfies condition ((S_)), where the last follows from the fact that F is continuous and satisfies condition ((S_)) and T is bounded.