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Article: Approximating zero points of accretive operators with compact domains in general Banach spaces.
- Article from:
- Fixed Point Theory and Applications
- Article date:
- January 1, 2005
- Author:
CopyrightCOPYRIGHT 2005 Hindawi Publishing Corp. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces.
1. Introduction
Let E be a real Banach space, let C be a closed convex subset of E, let T be a nonexpansive mapping of C into itself, that is, [parallel][T.sub.x] - [T.sub.y][parallel] [less than or equal to] [parallel]x - y[parallel] for each x, y [member of] C, and let A [subset] E x E be an accretive operator. For r > 0, we denote by [J.sub.r] the resolvent of A, that is, [J.sub.r] = [(I + rA).sup.-1]. The problem of finding a solution ...