Sentence examples for more general iteration from inspiring English sources

In the applications, X may be the unit interval, or a Cantor set; or it may be an affine fractal, or even one of the more general iteration limits involving iterated function systems consisting of conformal maps.

The more general iteration policy embodied in S5 may also be adopted.

We intend to carry out the extraction of a suitable Ψ for our more general iteration schema with two finite families of mappings in another paper.

A more general iteration scheme is the Ishikawa iteration given by { y n = β n T x n + ( 1 − β n ) x n, x n + 1 = γ n T y n + ( 1 − γ n ) x n, (1.2).

A more general iteration scheme is the Halpern iteration, given by { u ∈ E, x 1 ∈ C chosen arbitrarily, y n = ( 1 − β n ) x n + β n T x n, x n + 1 = α n u + ( 1 − α n ) y n, (1.3).

A more general iteration scheme of one-step Halpern iteration is two-step Halpern iteration given by { u ∈ C, x 1 ∈ C chosen arbitrarily, y n = ( 1 − β n ) x n + β n T x n, x n + 1 = α n u + ( 1 − α n ) y n, (1.3).

Corollary 2.10 extends, improves, and unifies Theorem 4 in [3], Theorem 2 in [7] and [8] in the following ways: (i the Mann iteration method in [7, 8], and Ishikawa iteration method in [3] are replaced by the more general Ishikawa iteration method with errors; (ii the nonexpansive mappings in [3, 7, 8] are replaced by the more general quasi-nonexpansive mappings.

Thus, iteration process (1.6) is more general than the iteration process (1.1)–(1.5) and iteration process of Khan [11].

In 1974, Ishikawa [34] introduced an iteration process which, in some sense, is more general than Mann iteration and which converges, under this setting, to a fixed point of T.

For those interested, see Mathieu, 1998 and Rodych, 2011, where it is not so clear that Wittgenstein did not have the more general notion of iteration.

However, the whole viscosity iteration is much more general than the iterative equation (2.1).