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The implicit midpoint rule for nonexpansive mappings
Journal article   Open access  Peer reviewed

The implicit midpoint rule for nonexpansive mappings

Maryam A. Alghamdi, Mohammad Ali Alghamdi, Naseer Shahzad and Hong-Kun Xu
Fixed point theory and applications (Hindawi Publishing Corporation), Vol.2014(1), pp.1-9
09/04/2014
DOI: https://doi.org/10.1186/1687-1812-2014-96

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
The implicit midpoint rule (IMR) for nonexpansive mappings is established. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a Hilbert space. Applications to the periodic solution of a nonlinear time-dependent evolution equation and to a Fredholm integral equation are included.
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https://doi.org/10.1186/1687-1812-2014-96View
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