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Moreover, the canonical rough paths of finite dimensional approximating Wiener processes converge to the enhanced Wiener process.
Let be given by Then, the modified doubly Mann's iteration process with errors converges to the fixed point, and both Picard and Mann iteration processes converge to the same point too.
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Two adjacent recursive processes converging to the mean value of a real-valued convex function are given.
In the calculation performed here, both processes converged to the same numerical value.
Ideally, this process converges to a shared common result.
Here, the optimization process converges to an acceptable solution with a certain degree of freedom.
It is proved, when the data are compatible, this fixed point process converges to the Cauchy problem solution.
The optimization process converges to a feasible solution s t d≃0 (highlighted in blue in Table 2).
Taking initial guess x 0 = 0.6 (away from the fixed point), the Picard process converges to a fixed point in 8 iterations, the Mann process converges in 75 iterations, the Ishikawa process converges in 38 iterations, the Noor process converges in 27 iterations, the Agarwal et al. process converges in 6 iterations and the S-iterative process converges in 6 iterations.
For x 0 = 0.8, the Picard process converges to a fixed point in 8 iterations, the Mann process converges in 69 iterations, the Ishikawa process converges in 34 iterations, the Noor process converges in 24 iterations, the Agarwal et al. process converges in 7 iterations and the S-iterative process converges in 6 iterations.
For x 0 = 0.8, the Picard process converges to a fixed point in 4 iterations, the Mann process converges in 36 iterations, the Ishikawa process converges in 22 iterations, the Noor process converges in 5 iterations and the Agarwal et al. as well as the S-iterative processes converge in 3 iterations.
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