61 citations · 113 across the 19 of their papers we have counts for
20 papers
Order preserving and order reversing operators on the class of -convex functions in complete random normed modules
Mingzhi Wu, Tiexin Guo, Long Long
Based on both the fundamental theorem of affine geometry in regular -modules and the recent progress in random convex analysis, this paper characterizes the stable fully order…
Some nonlinear characterizations of reflexive Banach spaces
Yan Tang, Shiqing Zhang, Tiexin Guo
It is well known that in the calculus of variations and in optimization there exist many formulations of the fundamental propositions on the attainment of the infima of sequentiall…
The fundamental theorem of affine geometry in regular -modules
Mingzhi Wu, Tiexin Guo, Long Long
Let be a probability space and the algebra of equivalence classes of real-valued random variables defined on . A left m…
The noncompact Schauder fixed point theorem in random normed modules and its applications
Tiexin Guo, Yachao Wang, Hong-kun Xu +2
Motivated by the randomized version of the classical Bolzano--Weierstrass theorem, in this paper we first introduce the notion of a random sequentially compact set in a random norm…
The Hille-Yosida generation theorem for almost surely bounded --semigroups of continuous module homomorphisms
Xia Zhang, Ming Liu, Tiexin Guo
In this paper, we first study some properties peculiar to --semigroups of continuous module homomorphisms and give a characterization for such a --semigroup to be alm…
Optimization of conditional convex risk measures
Tiexin Guo
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhap…
On ----stability in random metric spaces and its applications
Tiexin Guo, Erxin Zhang, Yachao Wang +1
In 2010, the first author of this paper introduced the notion of --stability for a nonempty subset of an --module in [T.X. Guo, Relations between some basic…
--convex compactness and random normal structure in
Tiexin Guo, Erxin Zhang, Yachao Wang +1
Let be a Banach space, a probability space and the set of equivalence classes of strong random elements (or strongly measur…
Two fixed point theorems in complete random normed modules and their applications to backward stochastic equations
Tiexin Guo, Erxin Zhang, Yachao Wang +1
This paper first proves two fixed point theorems in complete random normed modules, which are respectively the random generalizations of the classical Banach's contraction mapping…
--convex compactness and its applications to random convex optimization and random variational inequalities
Tiexin Guo, Erxin Zhang, Yachao Wang +1
In 2010, Gordan Žitković introduced the notion of convex compactness for a convex subset of a linear topological space and gave some important applications to both nonlinear analys…
On random convex analysis
Tiexin Guo, Erxin Zhang, Mingzhi Wu +3
Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments suc…
The -extension of an -normed module
Mingzhi Wu, Tiexin Guo
In this paper, we embed each -normed module into an appropriate and unique complete random normed module so that the properties of are closely related to th…
Random convex analysis (I): separation and Fenchel-Moreau duality in random locally convex modules
Tiexin Guo, Shien Zhao, Xiaolin Zeng
To provide a solid analytic foundation for the module approach to conditional risk measures, our purpose is to establish a complete random convex analysis over random locally conve…
Random convex analysis (II): continuity and subdifferentiability theorems in --pre--barreled random locally convex modules
Tiexin Guo, Shien Zhao, Xiaolin Zeng
In this paper, we continue to study random convex analysis. First, we introduce the notion of an --pre--barreled module. Then, we develop the theory of random duality under th…
A counterexample shows that not every locally --convex topology is necessarily induced by a family of --seminorms
Mingzhi Wu, Tiexin Guo
This paper constructs a counterexample showing that not every locally --convex topology is necessarily induced by a family of --seminorms. Random convex analysis is the a…
On random convex analysis -- the analytic foundation of the module approach to conditional risk measures
Tiexin Guo, Shien Zhao, Xiaolin Zeng
To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex mod…
Ekeland's Variational Principle for An Valued Function on A Complete Random Metric Space
Tiexin Guo, Yujie Yang
Motivated by the recent work on conditional risk measures, this paper studies the Ekeland's variational principle for a proper, lower semicontinuous and lower bounded $\bar{L}^{0}-…
The Algebraic Structure of Finitely Generated -Modules and the Helly Theorem in Random Normed Modules
Tiexin Guo, Guang Shi
Let be the scalar field of real numbers or complex numbers and the algebra of equivalence classes of valued random variables defined on a probability…
Recent progress in random metric theory and its applications to conditional risk measures
Tiexin Guo
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sect…
A comprehensive connection between the basic results and properties derived from two kinds of topologies for a random locally convex module
Tiexin Guo
The purpose of this paper is to make a comprehensive connection between the basic results and properties derived from the two kinds of topologies (namely the topology intro…