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• W2893094212 abstract "Abstract Let E be a uniformly convex and uniformly smooth real Banach space, and let E * be its dual. Let A : E → 2 E * be a bounded maximal monotone map. Assume that A −1 (0) ≠ Ø. A new iterative sequence is constructed which converges strongly to an element of A −1 (0). The theorem proved complements results obtained on strong convergence of the proximal point algorithm for approximating an element of A −1 (0) (assuming existence) and also resolves an important open question. Furthermore, this result is applied to convex optimization problems and to variational inequality problems. These results are achieved by combining a theorem of Reich on the strong convergence of the resolvent of maximal monotone mappings in a uniformly smooth real Banach space and new geometric properties of uniformly convex and uniformly smooth real Banach spaces introduced by Alber, with a technique of proof which is also of independent interest." @default.
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• W2893094212 date "2018-09-26" @default.
• W2893094212 modified "2023-09-27" @default.
• W2893094212 title "A Strong Convergence Theorem for an Iterative Method for Finding Zeros of Maximal Monotone Maps with Applications to Convex Minimization and Variational Inequality Problems" @default.
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• W2893094212 doi "https://doi.org/10.1017/s0013091518000366" @default.
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