□ We start with the observation that stability (A1) and reduction (A2) lead to a perturbed contraction of the error estimator in each step of the adaptive loop.
As observed from Table 1, the contraction factors of errors (frac{|nabla u-u_{h})|_{0}}{|nabla u|_{0}}), (frac{|nabla u-u_{h})| _{0}}{|nabla T|_{0}}), and (frac{|p-p_{h}|_{0}}{|p|_{0}}) become smaller and smaller as the mesh is refined, and the orders of these relative errors are arou|_{(frac{1}{4}) as the mesh is refined once.
Secondly, if the amplitude of the background noise is greater than the fetal heartbeat during the uterine contractions, the resulting error signal will not contain the FECG accurately.
Namely, we apply Mizoguchi and Takahashi's fixed point theorem of contraction mappings and an error bound of a system of linear inequalities to establish existence conditions for a variational relation problem in which the variational relation linearly depends on the decision variable.
Measurements confirmed that the length and diameter of the modules in any single batch were highly reproducible, both before and after contraction, to a standard error within 5% of the mean for that batch.
Grouping all contractions gave a reconstruction error of ~19%.
In the proof of Theorem 3.1, we employ the new Picard-Mann iterative approximation with mixed errors for contraction operators, which differs from the method proposed in Ayadi et al. [1] for showing that problem (3.4) has a weak solution.
Furthermore, as an application, we explore iterative approximation of solutions for an elliptic boundary value problem in Hilbert spaces by using the new Picard-Mann iterative methods with mixed errors for contraction operators.
However, how does one obtain stability analysis when the Picard-Mann hybrid iterative scheme due to Khan [18] is generalized for two different nonexpansive and contraction operators and one involves errors or mixed errors?
