Hybrid viscosity-like approximation methods for nonexpansive mappings in Hilbert spaces
- Ceng, Lu-Chuan
- Guu, Sy-Ming
- Yao, Jen-Chih
DOIAbstract
AbstractConsider on a real Hilbert space H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 0<α<1, and two strongly positive linear bounded operators A,B with coefficients γ̄∈(0,1) and β>0, respectively. Let 0<γα<β. We introduce a general iterative algorithm defined by xn+1≔(I−λn+1A)Txn+λn+1[Txn−μn+1(BTxn−γf(xn))],∀n≥1, with μn→μ(n→∞), and prove the strong convergence of the iterative algorithm to a fixed point x̃∈Fix(T)≕C which is the unique solution of the variational inequality (for short, V I(A−I+μ(B−γf),C)): 〈[A−I+μ(B−γf)]x̃,x−x̃〉≥0,∀x∈C. On the other hand, assume C is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on H. We devise another iterative algorithm which gener...
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