Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^*, and C be a nonempty closed convex subset of E. Let {T(t) : t ≥ 0} be a nonexpansive semigroup on...Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^*, and C be a nonempty closed convex subset of E. Let {T(t) : t ≥ 0} be a nonexpansive semigroup on C such that F :=∩t≥0 Fix(T(t)) ≠ 0, and f : C → C be a fixed contractive mapping. If {αn}, {βn}, {an}, {bn}, {tn} satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as:{yn=αnxn+(1-αn)T(tn)xn,xn=βnf(xn)+(1-βn)yn{u0∈C,vn=anun+(1-an)T(tn)un,un+1=bnf(un)+(1-bn)vnWe prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix(T(t)), which is a unique solution in F to the following variational inequality:〈(I-f)q,j(q-u)〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 (2002)], and Kim and XU [Nonlear Analysis, 61, 51-60 (2005)] and Chen and He [Appl. Math. Lett., 20, 751-757 (2007)].展开更多
在一致光滑和2-一致凸Banach空间框架下,引入广义杂交投影算法,建立了该算法强收敛于3个集合(平衡问题的解集、变分不等式的解集和两闭拟φ-非扩张映射公共不动点集)的公共解的新结果.所得结果本质改进和推广了2005年Matsushita和Takaha...在一致光滑和2-一致凸Banach空间框架下,引入广义杂交投影算法,建立了该算法强收敛于3个集合(平衡问题的解集、变分不等式的解集和两闭拟φ-非扩张映射公共不动点集)的公共解的新结果.所得结果本质改进和推广了2005年Matsushita和Takahashi、2009年Qin X L,Cho Y Je和Kang S M等人的相应新结果.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 10771050)supported by the Higher Education Commission, Pakistan, through Research Grant No. 1-29/HEC/HRD/2005/90
文摘Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^*, and C be a nonempty closed convex subset of E. Let {T(t) : t ≥ 0} be a nonexpansive semigroup on C such that F :=∩t≥0 Fix(T(t)) ≠ 0, and f : C → C be a fixed contractive mapping. If {αn}, {βn}, {an}, {bn}, {tn} satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as:{yn=αnxn+(1-αn)T(tn)xn,xn=βnf(xn)+(1-βn)yn{u0∈C,vn=anun+(1-an)T(tn)un,un+1=bnf(un)+(1-bn)vnWe prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix(T(t)), which is a unique solution in F to the following variational inequality:〈(I-f)q,j(q-u)〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 (2002)], and Kim and XU [Nonlear Analysis, 61, 51-60 (2005)] and Chen and He [Appl. Math. Lett., 20, 751-757 (2007)].
文摘在一致光滑和2-一致凸Banach空间框架下,引入广义杂交投影算法,建立了该算法强收敛于3个集合(平衡问题的解集、变分不等式的解集和两闭拟φ-非扩张映射公共不动点集)的公共解的新结果.所得结果本质改进和推广了2005年Matsushita和Takahashi、2009年Qin X L,Cho Y Je和Kang S M等人的相应新结果.