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Strong convergence of an iterative sequence for maximal monotone operators in a Banach space. (English) Zbl 1064.47068
Authors’ abstract: “We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by S. Kamimura and W. Takahashi in a Hilbert space [J. Approximation Theory 106, No. 2, 226–240 (2000; Zbl 0992.47022)]. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.”

MSC:
47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
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