Exact(18)
If the Ishikawa iteration (1.6) converges strongly to, then setting, in (1.6), we can get the convergence of Mann iteration (1.5).
end{aligned} Hence, using (12), we get the convergence (13).
As applications, we get the convergence criteria under the Kantorovich's condition and the γ-condition, respectively.
Using the Chebyshev-Markov inequality, we can also get the convergence in probability.
Then we get the convergence, and the convergence order in spatial direction is just two.
We also get the convergence rate of the subgradient extragradient methods with BP (5.15) and (5.16).
Similar(42)
For example, in 2003, Chidume et al. [16] introduced the following modified Mann iteration process and got the convergence theorems for asymptotically nonexpansive nonself-mapping: x 1 ∈ C, x n + 1 = P [ α n x n + ( 1 - α n ) T ( P T ) n - 1 x n ], n ≥ 1. (1.2).
In order to get the global convergence of Algorithm 1, we give the following assumptions.
We get the following convergence theorem for the split feasibility problem by using Theorem 2.2.
It shows that the proposed SXFEM can get the optimal convergence order.
We get the following convergence theorem for the linear inverse problem by using Theorem 2.2.
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