Mingzhi Wu

activity

20152022

most citedA counterexample shows that not every locally

L^{0}

--convex topology is necessarily induced by a family of

L^{0}

--seminorms

11 citations · 14 across the 8 of their papers we have counts for

collaborators

9 papers

math.FA2022

Order preserving and order reversing operators on the class of $L^{0}$ -convex functions in complete random normed modules

Mingzhi Wu, Tiexin Guo, Long Long

Based on both the fundamental theorem of affine geometry in regular $L^{0}$ -modules and the recent progress in random convex analysis, this paper characterizes the stable fully order…

math.FA2021

The fundamental theorem of affine geometry in regular $L^{0}$ -modules

Mingzhi Wu, Tiexin Guo, Long Long

Let $(Ω, F, P)$ be a probability space and $L^{0} (F)$ the algebra of equivalence classes of real-valued random variables defined on $(Ω, F, P)$ . A left m…

math.FA2019

On $L^{0}$ -convex compactness in random locally convex modules

Mingzhi Wu, Xiaolin Zeng, Shien Zhao

For the study of some typical problems in finance and economics, Žitković %[G. Žitković, Convex compactness and its applications, Math. Finan. Eco., 3(1)(2010) 1--12] introduced co…

math.AG2018

The fundamental theorem of affine geometry in $(L^{0})^{n}$

Mingzhi Wu, Long Long

Let $L^{0}$ be the algebra of equivalence classes of real valued random variables on a given probability space, and $(L^{0})^{n}$ the $n$ -ary Cartesian power of $L^{0}$ for each integer $n…

math.FA2017★ 1 cited

$L^{0}$ --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…

math.FA2016★ 1 cited

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…

math.FA2015★ 1 cited

The $L^{0}$ -extension of an $L^{\infty}$ -normed module

Mingzhi Wu, Tiexin Guo

In this paper, we embed each $L^{\infty}$ -normed module $E$ into an appropriate and unique complete random normed module $E_{0}$ so that the properties of $E$ are closely related to th…

math.FA2015

Some results on the Orlicz space generated from a random normed module

Mingzhi Wu, Long Long, Xiaolin Zeng

Noting the important role the abstract $L^{p}$ space has played in the development of random normed modules, in this paper we introduce and study the Orlicz space generated from a ra…

math.FA2015★ 11 cited

A counterexample shows that not every locally $L^{0}$ --convex topology is necessarily induced by a family of $L^{0}$ --seminorms

Mingzhi Wu, Tiexin Guo

This paper constructs a counterexample showing that not every locally $L^{0}$ --convex topology is necessarily induced by a family of $L^{0}$ --seminorms. Random convex analysis is the a…

Order preserving and order reversing operators on the class of L0-convex functions in complete random normed modules

The fundamental theorem of affine geometry in regular L0-modules

On L0-convex compactness in random locally convex modules

The fundamental theorem of affine geometry in (L0)n

L0--convex compactness and its applications to random convex optimization and random variational inequalities