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An extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces. (English) Zbl 1186.47076
From the summary: We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
47J20 Variational and other types of inequalities involving nonlinear operators (general)
Full Text: DOI EuDML
[1] doi:10.1137/0314056 · Zbl 0358.90053 · doi:10.1137/0314056
[2] doi:10.1137/S105262340139611X · Zbl 1101.90083 · doi:10.1137/S105262340139611X
[3] doi:10.1007/s00013-003-0508-7 · Zbl 1067.47080 · doi:10.1007/s00013-003-0508-7
[4] doi:10.1007/s11228-004-8196-4 · Zbl 1078.47050 · doi:10.1007/s11228-004-8196-4
[5] doi:10.1016/j.jmaa.2007.07.019 · Zbl 1129.49012 · doi:10.1016/j.jmaa.2007.07.019
[6] doi:10.1016/0362-546X(91)90200-K · Zbl 0757.46033 · doi:10.1016/0362-546X(91)90200-K
[7] doi:10.1155/S1085337504309036 · Zbl 1064.47068 · doi:10.1155/S1085337504309036
[8] doi:10.1090/S0002-9947-1970-0282272-5 · doi:10.1090/S0002-9947-1970-0282272-5
[9] doi:10.1007/BF03007664 · Zbl 0352.47023 · doi:10.1007/BF03007664
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