The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Se...The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.展开更多
For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ...For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ≥ 1,n ≥ 1 are equivalent.Both the identically distributed and the nonidentically distributed cases are treated.In the main theorems,no assumptions are made concerning the geometry of the underlying Banach space.These theorems are applied to obtain Kolmogorov,Brunk–Chung,and Marcinkiewicz–Zygmund type strong laws of large numbers for double sums in Rademacher type p（1 ≤ p ≤ 2） Banach spaces.展开更多
The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable B...The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved.展开更多
文摘The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.
基金supported by the Vietnam Institute for Advanced Study in Mathematics(VIASM)the Vietnam National Foundation for Sciences and Technology Development NAFOSTED(Grant No.101.01.2012.13)supported by NAFOSTED(Grant No.101.03.2012.17)
文摘For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ≥ 1,n ≥ 1 are equivalent.Both the identically distributed and the nonidentically distributed cases are treated.In the main theorems,no assumptions are made concerning the geometry of the underlying Banach space.These theorems are applied to obtain Kolmogorov,Brunk–Chung,and Marcinkiewicz–Zygmund type strong laws of large numbers for double sums in Rademacher type p（1 ≤ p ≤ 2） Banach spaces.
基金Project supported by the Natural Science Foundation of Yibin University (No. 2011Z03)
文摘The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved.
