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Ergodicity of the implicit midpoint rule for nonexpansive mappings
Journal article   Open access  Peer reviewed

Ergodicity of the implicit midpoint rule for nonexpansive mappings

Hong-Kun Xu, Maryam A Alghamdi and Naseer Shahzad
Journal of inequalities and applications, Vol.2015(1), pp.1-9
06/01/2015
DOI: https://doi.org/10.1186/1029-242X-2015-4

Abstract

Analysis Applications of Mathematics general Mathematics Mathematics and Statistics Thematic series on Nonlinear Analysis and Optimization
We prove a mean ergodic theorem for the implicit midpoint rule for nonexpansivemappings in a Hilbert space. We obtain weak convergence for the general case andstrong convergence for certain special cases. MSC: 47J25, 47N20, 34G20, 65J15.
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https://doi.org/10.1186/1029-242X-2015-4View
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