In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration ...In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.展开更多
The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps under Benson proper efficiency. Let W(u) = Pmin[G(u),S],y∧∈W(u∧). It is shown that,...The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps under Benson proper efficiency. Let W(u) = Pmin[G(u),S],y∧∈W(u∧). It is shown that, under some conditions, DW(u∧,y∧) Pmin[DG(u∧,y∧),S] , and under some other conditions, DW(u∧,y∧) Pmin[DG(u∧,y∧),S].展开更多
文摘In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.
基金Supported by the National Natural Science Foundation of China(69972036)
文摘The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps under Benson proper efficiency. Let W(u) = Pmin[G(u),S],y∧∈W(u∧). It is shown that, under some conditions, DW(u∧,y∧) Pmin[DG(u∧,y∧),S] , and under some other conditions, DW(u∧,y∧) Pmin[DG(u∧,y∧),S].
