Sentence examples for extended iteration from inspiring English sources

New technical shades of meaning began appearing in the late 1960s, as programmers extended iteration to broader computational problems.

An extended iteration method for calculating the periodic solutions of nonlinear oscillator equations is given.

Recently, Kohsaka and Takahashi [18] extended iteration (1.9) to obtain a weak convergence theorem for common fixed points of a finite family of relatively nonexpansive mappings by the following iteration: (1.10).

Storey's method for multiple hypothesis testing "the Optimal Discovery Procedure ODPDP) minimising the false discovery rate (FDR) and giving p-values and q-values (estimates of FDR) for each test, was extended by iteration to enforce consistency between the p-values of the tests and the binary parameters defining which data points contribute to the fitted null hypothesis.

Further extended viscosity iteration schemes with nonexpansive mappings based on the above one have been investigated in [9, 10, 12 18], while proving the common existence of unique fixed points for the related schemes and the strong convergence of the iterations to those points for any arbitrary initial conditions.

They proved in [12] that the sequence { x n } converges weakly to a common fixed point of T n, n = 1, 2, …, N. Later on Osilike and Akuchu [13], and Chen et al. [14] extended the iteration process (1.3) to a finite family of asymptotically pseudo-contractive mapping and a finite family of continuous pseudo-contractive self-mapping, respectively.

The schemes (3.1), (4.4), and (5.1) generalize and extend several iteration processes from literature (see [7, 8, 17, 21 25] and others).

Very recently, Qin et al. [6] extend the iteration process (1.7) from a single relatively nonexpansive mapping to two relatively quasi-nonexpansive mappings: (1.8).

To extend this iteration to a Banach space, the concepts of relatively nonexpansive mappings and quasi-ϕ-nonexpansive mappings have been introduced (see [8 11] and [12]).

The purpose of this paper is to extend the iteration scheme of multivalued nonexpansive mappings from a Banach space to a hyperbolic space by proving Δ-convergence theorems for two multivalued nonexpansive mappings in terms of mixed type iteration processes to approximate a common fixed point of two multivalued nonexpansive mappings in hyperbolic spaces.

To extend this iteration to a Banach space, the concept of relatively nonexpansive mappings and quasi-ϕ-nonexpansive mappings have been introduced by Aoyama et al. [8], Chang et al. [9, 10], Chidume et al. [11], Matsushita et al. [12 14], Qin et al. [15], Song et al. [16], Wang et al. [17] and others.