Sentence examples for by the iterative sequence from inspiring English sources

So, by the iterative sequence of Algorithm 3.1, we have ∥ x k j − x 0 ∥ ≤ ∥ x ¯ − x 0 ∥.

So, by the iterative sequence of Algorithm 3.1 we have biglVert x^{k_{j}}-x^{0}bigrVert leqbiglVert x^{ast}-x^{0}bigrVert.

In this article, we are concerned with the convergence to a common fixed point for a finite family of nonself uniformly quasi-Lipschitzian mappings in Banach spaces by using the iterative sequence (1.2).

In this paper, motivated by the iterative sequences (1.6) given by Saejung in [8] and Ishikawa [10], we introduce the modified Ishikawa iterative scheme for two nonexpansive semigroups in Hilbert spaces.

By Theorem 3.3, the iterative sequence ({x_{n}}) generated by (4.9) converges strongly to ({x^ = {P_{operatorname{VI}(C,A)}}theta=P_{operatorname{Fix}(T }theta).

By Theorem 3.2, the iterative sequence ({x_{n}}) converges strongly to ({x^ = {P_{operatorname{VI}(C,A)}}theta).

In 1967, Halpern [1] introduced an explicit iterative scheme for a nonexpansive mapping on a subset of a Hilbert space by taking any points and defined the iterative sequence by (12).

This algorithm was first introduced by Martinet [7] and then generally studied by Rockafellar [8], who devised the iterative sequence { x n } by x n + 1 = J α n A x n + e n, n ∈ N, (6).

By the definition of the iterative sequence (1.10), we have (3.9).

By virtue of new analytical techniques, we prove that the iterative sequence generated by these iterative procedures converges to the solution of the split feasibility problem which is the best close to a given point.

For any,, compute the iterative sequence by (3.5).