In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T i...In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.展开更多
In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing th...In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.展开更多
<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the ...<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0＜α≤b_n+c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~'+c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.展开更多
设1<p2,0<α1,X是p一致可光滑空间的Banach空间,则对每个X值拟鞅f=(fn)n≥0∈pHασ(X)存在分解fn=sum form k∈Z to μkank(n≥0),并且‖f‖pHασ(X)+‖R(f)‖α～inf(sum form k∈Z to μkα)1/α,这里ak=(ank)n5≥0(k∈Z)是一...设1<p2,0<α1,X是p一致可光滑空间的Banach空间,则对每个X值拟鞅f=(fn)n≥0∈pHασ(X)存在分解fn=sum form k∈Z to μkank(n≥0),并且‖f‖pHασ(X)+‖R(f)‖α～inf(sum form k∈Z to μkα)1/α,这里ak=(ank)n5≥0(k∈Z)是一列(1,α,∞;p)拟鞅原子,并且在L1中收敛,supk∈Z‖ak*‖α<∞,(μk)k∈Z∈lα是非负实数列.对于拟鞅空间pHαS(X)和qKα(X)成立类似的结果.此外,利用拟鞅原子分解定理,证明了几个拟鞅不等式.展开更多
基金The project supported by the Science and Technology Development Fund of Shanghai Higher Learning
文摘In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.
基金supported by the National Science Foundation of China(11271161)
文摘In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.
基金This work was supported partially by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions by Ministry of Educationthe Department Fund of Science and Technology in Shanghai Higher Education Institutionsthe Special Funds for Major Specialities by the Shanghai Education Committee.
文摘<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0＜α≤b_n+c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~'+c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.
文摘设1<p2,0<α1,X是p一致可光滑空间的Banach空间,则对每个X值拟鞅f=(fn)n≥0∈pHασ(X)存在分解fn=sum form k∈Z to μkank(n≥0),并且‖f‖pHασ(X)+‖R(f)‖α～inf(sum form k∈Z to μkα)1/α,这里ak=(ank)n5≥0(k∈Z)是一列(1,α,∞;p)拟鞅原子,并且在L1中收敛,supk∈Z‖ak*‖α<∞,(μk)k∈Z∈lα是非负实数列.对于拟鞅空间pHαS(X)和qKα(X)成立类似的结果.此外,利用拟鞅原子分解定理,证明了几个拟鞅不等式.
