Weak and Strong Convergence of Solutions to Accretive Operator Inclusions and Applications |
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| Authors: | Shoji Kamimura and Wataru Takahashi |
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| Institution: | (1) Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo, 152-8552, Japan;(2) Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo, 152-8552, Japan |
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| Abstract: | Our purpose in this paper is to approximate solutions of accretive operators in Banach spaces. Motivated by Halpern's iteration and Mann's iteration, we prove weak and strong convergence theorems for resolvents of accretive operators. Using these results, we consider the convex minimization problem of finding a minimizer of a proper lower semicontinuous convex function and the variational problem of finding a solution of a variational inequality. |
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| Keywords: | accretive operator resolvent iteration strong convergence weak convergence |
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