Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces
Keyword(s):
Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces are studied. Consider a nonexpansive self-mappingTof a closed convex subsetCof a CAT(0) spaceX. Suppose that the set Fix(T)of fixed points ofTis nonempty. For a contractionfonCandt∈(0,1), letxt∈Cbe the unique fixed point of the contractionx↦tf(x)⊕(1-t)Tx. We will show that ifXis a CAT(0) space satisfying some property, then{xt}converge strongly to a fixed point ofTwhich solves some variational inequality. Consider also the iteration process{xn}, wherex0∈Cis arbitrary andxn+1=αnf(xn)⊕(1-αn)Txnforn≥1, where{αn}⊂(0,1). It is shown that under certain appropriate conditions onαn,{xn}converge strongly to a fixed point ofTwhich solves some variational inequality.
2015 ◽
Vol 4
(2)
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pp. 299
2007 ◽
Vol 14
(4)
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pp. 405-420
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2007 ◽
Vol 191
(1)
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pp. 155-163
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2013 ◽
Vol 2013
(1)
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