Sentence examples for using the iterative scheme from inspiring English sources

This computational remark suggests the possibility of using the iterative scheme also in case the condition L ≥ L 0 fails; however, its convergence properties should be theoretically analyzed.

The optimal number of fitting points was determined using the iterative scheme proposed in [ 57].

In this paper, we show an analogous result to Theorem 1.1 using the iterative scheme (1) in a complete CAT ( 1 ) space with two quasinonexpansive and Δ-demiclosed mappings.

Considering u fixed, compute f i 1 and f i 2 by using formula (3.2); Considering f i 1 and f i 2 fixed, update u by using the iterative schemes of minimization problem (3.3).

That is, we minimize the energy functional E by alternating the following steps: (1) Considering u fixed, compute f i 1 and f i 2 by using formula (3.2);   (2) Considering f i 1 and f i 2 fixed, update u by using the iterative schemes of minimization problem (3.3).  .

Question 1.1 Is there any strong convergence theorem of Halpern type for nonspreading mappings in a Hilbert space H? By using the iterative schemes proposed by Moudafi [8], Iemoto and Takahashi [18] studied the approximation of common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space and proved the following strong convergence theorem.

The proof of Theorem 3.2 shows that the properties of projections used in the iterative scheme do not interact with the properties of mappings.

The proof of Theorem 3.1 shows that the properties of generalized projections used in the iterative scheme do not interact with the properties of mappings {T λ }.

Theorem 3.1 extends and improves the result of Chang et al. [11, 15] from weak convergence to strong convergence by using the modified iterative scheme that we propose.

Recently, some authors by using the block iterative scheme to establish strong convergence theorems for a finite family of relativity nonexpansive mappings in Hilbert space or finite-dimensional Banach space (see, e.g., Aleyner and Reich [12], Plubtieng and Ungchittrakool [13, 14]) or uniformly smooth and uniformly convex Banach spaces (see, e.g., Sahu et al. [15] and Ceng et al. [16 18]).

Using the above iterative schemes, Panyanak [4] generalized the result proved by [3].