7 papers
Stable topology and stable compactness
Tiexin Guo, Qiang Tu, Xiaohuan Mu +3
To solve a large class of noncompact problems ubiquitous in random functional analysis and its applications, most of compactness-based fundamental theorems established for normed s…
A random demiclosedness principle for random asymptotically nonexpansive mappings
Yuanyuan Sun, Tiexin Guo, Qiang Tu
By making full use of the inherent connection between the theory of random conjugate spaces and the theory of classical conjugate spaces, in this paper we establish a random demicl…
Survey of Metric fixed point theory in random functional analysis
Tiexin Guo, Qiang Tu, Xiaohuan Mu +1
Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces…
The random Kakutani fixed point theorem in random normed modules
Qiang Tu, Xiaohuan Mu, Tiexin Guo +2
Based on the recently developed theory of random sequential compactness, we prove the random Kakutani fixed point theorem in random normed modules: if G is a random sequentially co…
A new complete proof of the random Brouwer fixed point theorem and its implied consequences of unification
Qiang Tu, Xiaohuan Mu, Tiexin Guo +1
We first establish a general random Sperner lemma by presenting a completely new approach for the theory of -simplicial subdivisions of -simplexes. Based on this, we…
Common fixed point theorems for a commutative family of nonexpansive mappings in complete random normed modules
Xiaohuan Mu, Qiang Tu, Tiexin Guo +1
In this paper, we first introduce and study the notion of random Chebyshev centers. Further, based on the recently developed theory of stable sets, we introduce the notion of rando…
The relations among the notions of various kinds of stability and their applications
Tiexin Guo, Xiaohuan Mu, Qiang Tu
First, we prove that a random metric space can be isometrically embedded into a complete random normed module, as an application of which, it is easy to see that the notion of -…