Abstract
Let E be a nonempty closed uniformly convex and 2-uniformly smooth Banach space with dual E∗ and A : E∗ → E be Lipschitz continuous monotone mapping with A− 1(0) ≠ ∅. A new semi-implicit midpoint rule (SIMR) with the general contraction for monotone mappings in Banach spaces is established and proved to converge strongly to x∗ ∈ E, where Jx∗ ∈ A− 1(0). Moreover, applications to convex minimization problems, solution of Hammerstein integral equations, and semi-fixed point of a cluster of semi-pseudo mappings are included.
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The authors express their deep gratitude to the referees and the editor for their valuable comments and suggestions.
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This article was funded by the National Science Foundation of China (11471059)and Science and Technology Research Project of Chongqing Municipal Education Commission (KJ1706154)and the Research Project of Chongqing Technology and Business University (KFJJ2017069).
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Supported by the National Natural Science Foundation of China (11471059) and Science and Technology Research Project of Chongqing Municipal Education Commission (KJ 1706154)and the Research Project of Chongqing Technology and Business University (KFJJ2017069)
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Tang, Y., Bao, Z. New semi-implicit midpoint rule for zero of monotone mappings in Banach spaces. Numer Algor 81, 853–878 (2019). https://doi.org/10.1007/s11075-018-0574-3
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DOI: https://doi.org/10.1007/s11075-018-0574-3