Nonlinear Ergodic Theorem for Positively Homogeneous Nonexpansive Mappings in Banach Spaces |
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| Authors: | Wataru Takahashi Ngai-Ching Wong Jen-Chih Yao |
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| Affiliation: | 1. Department of Applied Mathematics , National Sun Yat-sen University , Kaohsiung , Taiwan;2. Department of Mathematical and Computing Sciences , Tokyo Institute of Technology , Tokyo , Japan wataru@is.titech.ac.jp;4. Center for Fundamental Science , Kaohsiung Medical University , Kaohsiung , Taiwan;5. Center for Fundamental Science , Kaohsiung Medical University , Kaohsiung , Taiwan;6. Department of Mathematics , King Abdulaziz University , Jeddah , Saudi Arabia |
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| Abstract: | Recently, two retractions (projections), which are different from the metric projection and the sunny nonexpansive retraction in a Banach space, were found. In this article, using nonlinear analytic methods and new retractions, we prove a nonlinear ergodic theorem for positively homogeneous and nonexpansive mappings in a uniformly convex Banach space. The limit points are characterized by using new retractions. |
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| Keywords: | Banach limit Banach space Fixed point Mean convergence Nonexpansive mapping Positively homogeneous mapping |
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