We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We ...We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.展开更多
The present paper is mainly concerned with several new types of fixed point theorems in different spaces such as cone metric spaces and fuzzy metric spaces. By using these obtained fixed point theorems, we then prove ...The present paper is mainly concerned with several new types of fixed point theorems in different spaces such as cone metric spaces and fuzzy metric spaces. By using these obtained fixed point theorems, we then prove the existence and uniqueness of the solutions to two classes of two-point ordinary differential equation problems.展开更多
In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive Banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized pr...In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive Banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K ： B → K and πK ： B^＊ → K. We also present some results in non-reflexive Banach spaces.展开更多
This article reports a study on the China-Canada-United States English Immersion(CCUEI)Moral Education and Social Studies(MESS)curriculum materials for elementary classes(Grades 3-6)with the aim of learning how the cu...This article reports a study on the China-Canada-United States English Immersion(CCUEI)Moral Education and Social Studies(MESS)curriculum materials for elementary classes(Grades 3-6)with the aim of learning how the curriculum addressed the dual goals of MESS content and English language learning.An analysis comparing the CCUEI third grade MESS textbook with an equivalent level Chinese textbook demonstrates how China’s national standards in MESS and English education can be met,and drawbacks encountered in the process.The CCUEI textbook was found to embrace grade level MESS content standards,but showed a varied degree of depth of content across standards.The textbook addressed all of the general goals of Level One English language learning(Grades 3-4)and most of the language skills indicators(16 out of 20).An additional in-depth teacher survey provided a user’s perspective on MESS materials.The teachers rated the textbook highly for its activity-centered format and knowledge-rich content.They emphasized the importance of teaching English language as preparation for the MESS content teaching,and asked for more systematic support in language teaching from curriculum materials.展开更多
文摘We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.
文摘The present paper is mainly concerned with several new types of fixed point theorems in different spaces such as cone metric spaces and fuzzy metric spaces. By using these obtained fixed point theorems, we then prove the existence and uniqueness of the solutions to two classes of two-point ordinary differential equation problems.
文摘In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive Banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K ： B → K and πK ： B^＊ → K. We also present some results in non-reflexive Banach spaces.
基金provided by two anonymous reviewers of an earlier version of this article.
文摘This article reports a study on the China-Canada-United States English Immersion(CCUEI)Moral Education and Social Studies(MESS)curriculum materials for elementary classes(Grades 3-6)with the aim of learning how the curriculum addressed the dual goals of MESS content and English language learning.An analysis comparing the CCUEI third grade MESS textbook with an equivalent level Chinese textbook demonstrates how China’s national standards in MESS and English education can be met,and drawbacks encountered in the process.The CCUEI textbook was found to embrace grade level MESS content standards,but showed a varied degree of depth of content across standards.The textbook addressed all of the general goals of Level One English language learning(Grades 3-4)and most of the language skills indicators(16 out of 20).An additional in-depth teacher survey provided a user’s perspective on MESS materials.The teachers rated the textbook highly for its activity-centered format and knowledge-rich content.They emphasized the importance of teaching English language as preparation for the MESS content teaching,and asked for more systematic support in language teaching from curriculum materials.
