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Can Theorem 2.4 be extended to the Ishikawa iteration method with errors?
In this section, we propose a modification of doubly Mann's iteration method with errors to have strong convergence.
In 1998, Xu [13] introduced an Ishikawa iteration method with errors which appears to be more satisfactory than the one introduced by Liu [12].
We obtain an iterative approximation of a zero point of a monotone operator generated by the shrinking projection method with errors in a Banach space.
We obtain iterative approximations of a zero point of a monotone operator generated by the shrinking projection method with errors in a Banach space.
Corollary 2.10 extends, improves, and unifies Theorem 4 in [3], Theorem 2 in [7] and [8] in the following ways: (i the Mann iteration method in [7, 8], and Ishikawa iteration method in [3] are replaced by the more general Ishikawa iteration method with errors; (ii the nonexpansive mappings in [3, 7, 8] are replaced by the more general quasi-nonexpansive mappings.
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These include the robust concept exploration method with error margin indices (RCEM-EMI) and the inductive design exploration method (IDEM).
The Analytically Reduced Chemistries (ARCs) are obtained using Directed Relation Graph method with Error Propagation (DRGEP) and Quasi-Steady-State (QSS) approximation.
The method with error estimates are contained in Section three.
In this paper, we study the shrinking projection method with error introduced by Kimura [10] (see also [12, 14]).
On the other hand, Kimura [10] introduced the following iterative scheme for finding a fixed point of nonexpansive mappings by the shrinking projection method with error in a Hilbert space: (Kimura [10]).
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