Sentence examples for processes with errors from inspiring English sources

In [3], Liu introduced the concepts of Ishikawa and Mann iterative processes with errors as follows.

Next, we prove strong convergence of iterative processes with errors for m-accretive operators.

We obtain strong convergence theorems of two modifications of Mann iteration processes with errors in the doubly sequence setting.

While it is known that the consideration of error terms in the iterative processes (1.5), (1.6) is an important part of the theory, it is also clear that the iterative processes with errors introduced by Liu in (I-a) and (I-b) are unsatisfactory.

Remark 17 Similar results can be found for the iteration processes with error terms, we omit the details.

(214 ., is called the Ishikawa iterative process with errors.

for, is called the Mann iterative process with errors.

Iterative process (1.14) can be replaced by Ishikawa iterative process with errors (1.9).

(iii) Iterative process (1.14) can be replaced by Ishikawa iterative process with errors (1.9).  .

Definition 1.5 (Ishikawa iterative process with errors in the sense of Xu [3]).

Open Question 1. Can the Ishikawa iterative process with errors (1.7) be extended to Theorem 1.7?