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Strong convergence studied by a hybrid type method for monotone operators in a Banach space. (English) Zbl 1220.47095

Summary: We study strong convergence for monotone operators. We first introduce a hybrid type algorithm for monotone operators. Next, we obtain a strong convergence theorem (Theorem 3.3) for finding a zero point of an inverse-strongly monotone operator in a Banach space. Finally, we apply our convergence theorem to the problem of finding a minimizer of a convex function.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
47J05 Equations involving nonlinear operators (general)
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