Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J...Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J_r denotes the resolvent(I+rA)^(-1)for r>1.Strong convergence of the algorithm {x_n} is obtained provided that E either has a weakly continuous duality map or is uniformly smooth.展开更多
In this note, we show that a Cowen-Douglas operator is strongly irreducible if and only if its commutant algebra rood its Jocobson radical is isomorphic to a closed subalgebra of H^∞ （D）, where D is the open unit d...In this note, we show that a Cowen-Douglas operator is strongly irreducible if and only if its commutant algebra rood its Jocobson radical is isomorphic to a closed subalgebra of H^∞ （D）, where D is the open unit disk, and H^∞（D） denotes the collection of bounded holomorphic functions on D.展开更多
Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T ： K →K be a uniformly continuous pseudocontractive mapping. Suppose every close...Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T ： K →K be a uniformly continuous pseudocontractive mapping. Suppose every closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Let {λn} C （0,1/2] be a sequence satisfying the conditions： （i） limn→∞λn=0; （ii） ∑n=0^∞ λn=∞. Let the sequence {xn} be generated from arbitrary x1∈K by xn＋1 = （1 -λn）xn ＋ λnTxn -λn（xn - x1）, n ≥ 1. Suppose limn→∞‖xn - Txn‖ = 0. Then {xn} converges strongly to a fixed point of T.展开更多
基金the National Natural Science Foundation of China （No. 10771050）.
文摘Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J_r denotes the resolvent(I+rA)^(-1)for r>1.Strong convergence of the algorithm {x_n} is obtained provided that E either has a weakly continuous duality map or is uniformly smooth.
基金the National Natural Science Foundation of China （No. 10571041） the Natural Science Foundation of Hebei Province （No. A2005000006）.
文摘In this note, we show that a Cowen-Douglas operator is strongly irreducible if and only if its commutant algebra rood its Jocobson radical is isomorphic to a closed subalgebra of H^∞ （D）, where D is the open unit disk, and H^∞（D） denotes the collection of bounded holomorphic functions on D.
基金the National Natural Science Foundation of China （No. 10771050）.
文摘Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T ： K →K be a uniformly continuous pseudocontractive mapping. Suppose every closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Let {λn} C （0,1/2] be a sequence satisfying the conditions： （i） limn→∞λn=0; （ii） ∑n=0^∞ λn=∞. Let the sequence {xn} be generated from arbitrary x1∈K by xn＋1 = （1 -λn）xn ＋ λnTxn -λn（xn - x1）, n ≥ 1. Suppose limn→∞‖xn - Txn‖ = 0. Then {xn} converges strongly to a fixed point of T.
