Sentence examples for normal iteration from inspiring English sources

Before entering this section, I recommend for readers to understand the Iteration Filter scheme [16] that is wholly different from the normal iteration sequence and shows the amazing memory reduction effect.

In an infinite-dimensional Hilbert space, the normal Mann iteration algorithm has only weak convergence.

Recall that the normal Mann iteration was introduced by Mann [1] in 1953.

Recently, construction of fixed points for nonlinear mappings via the normal Mann iteration has been extensively investigated by many authors.

In an infinite-dimensional Hilbert space, the normal Mann iteration algorithm has only weak convergence; see [14] for more details.

In an infinite-dimensional Hilbert space, the normal Mann iteration algorithm has only weak convergence, in general, even for nonexpansive mappings.

Attempts to modify the normal Mann iteration method (1.2) for nonexpansive mappings so that strong convergence is guaranteed have recently been made; see, for example, [2 9].

Since the Mann iterative algorithm only has weak convergence in infinite dimension spaces, many authors tried to modify the normal Mann iteration algorithm to have strong convergence for nonexpansive mappings.

We also remark here that many authors have been instigating the problem of modifying the normal Mann iteration process to have strong convergence for κ-strictly pseudocontractive mappings; see [24 27] and the references therein.

For any x 0 ∈ C, the normal Mann iteration { x n } is defined by x n + 1 = ( 1 − α n ) x n + α n T x n, n ≥ 0. (2.2).

The normal Mann iteration generates a sequence { x n } in the following manner: x 1 ∈ R, x n + 1 = ( 1 − α n ) x n + α n f ( x n ) (1.1).