Sentence examples for the modified iteration from inspiring English sources

The second part is devoted to the modified iteration methods and the integration of sensor signals into the iterative computations.

The second stage of the algorithm is the use of the modified iteration procedure based on Kirkpatrick approach leading to the direct current resistivity of the virtual sample.

In 2005, Kim and Xu [16] modified Mann's iteration scheme and the modified iteration method still works in a Banach space.

Now, consider the modified iteration process (2.1), one interesting problem is studying the stability of the iteration scheme ({x_{n}}) generated by (2.1).

In this paper, we introduce the modified iterations of Mann's type for nonexpansive mapping and asymptotically nonexpansive mapping to have the strong and weak convergence in a uniformly convex Banach space.

Now, we give a convergence theorem for continuous mappings on an arbitrary interval by using the following modified iteration method defined by Suantai [9].

For an appropriate and starting from an arbitrary initial point, we devise the following implicit, explicit, and modified iterations: (1.8).

In 2008, using the Mann iteration and the modified Ishikawa iteration, Zhou [3] obtained some weak and strong convergence theorems for -strict pseudocontractions in Hilbert spaces which extend the corresponding results in [2].

The modified Mann iteration and modified Ishikawa iteration are replaced by the modified Ishikawa iteration with errors introduced by Xu [17].

Remark 2.4 Theorem 2.1 extends, improves and unifies Theorems 3.1, 3.2, 3.3 of [13] and Theorem 3.5 of [14] in the following sense: (1) The modified Mann iteration and modified Ishikawa iteration are replaced by the modified Ishikawa iteration with errors introduced by Xu [17].

In this paper, motivated and inspired by the above results, we modify iteration process (1.4)–(1.11) by the new hybrid methods for countable families of asymptotically nonexpansive mappings and semigroups in a Hilbert space, and to prove strong convergence theorems.