反Banach空间内涉及广义混合似臣分不等式问题的双水平广义混合平衡问题

在自反Banach空间内,引入和研究了一类新的涉及广义混合似变分不等式问题的双水平广义混合平衡问题(BGMEP).首先,为了计算BGMEP的近似解,引入了一类辅助广义混合平衡问题(AGMEP).由使用一极小极大不等式,在没有任何强制条件的相当温和假设下,证明了AGMEP解的存在性和唯一性.利用辅助原理技巧,建议和分析了一类计算BGMEP的近似解的新迭代算法.在没有任何强制条件的相当温和假设下,证明了由算法生成的迭代序列的强收敛性.这些结果是新的并且推广了这一领域内某些最近结果.     

一类广义非线性隐拟变分包含

引入和研究了一类新的涉及集值极大单调映象的广义非线性隐拟变分包含.对此类变分包含在没有紧性假设下证明了解的存在定理.为寻求此类变分包含的近似解,建议和分析了一个新的迭代算法.给出了由新算法产生的迭代序列的收敛性.作为特殊情形,也讨论了在此领域内的某些已知结果.     

MAXIMAL ELEMENTS OF A FAMILY OF GB-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.     

A new equilibrium existence theorem of generalized game

ＡＮＥＷＥＱＵＩＬＩＢＲＩＵＭＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＯＦＧＥＮＥＲＡＬＩＺＥＤＧＡＭＥＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ）ＡＮＥＷＥＱＵＩＬＩＢＲＩＵＭＥＸＩＳＴＥＮＣＥＴＨＥ...     

Nonempty intersection theorems and system of generalized vector equilibrium problems in product G-convex spaces

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.     

Quasi-Equilibrium Problems and Constrained Multiobjective Games in Generalized Convex Space

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＸａｎｄＹｂｅｎｏｎｅｍｐｔｙｓｅｔｓａｎｄ2 ＸｂｅｔｈｅｆａｍｉｌｙｏｆａｌｌｓｕｂｓｅｔｓｏｆＸ .ＬｅｔＴ :Ｘ→Ｙｂｅａｓｉｎｇｌｅ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,Ａ :Ｘ→ 2 Ｘｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,ψ :Ｘ×Ｙ×Ｘ→Ｒ∪ ±∞ ａｎｄｆ:Ｘ×Ｙ→Ｒ∪ ±∞ ｂｅｔｗｏｆｕｎｃｔｉｏｎｓ.Ｔｈｅｇｅｎｅｒａｌｑｕａｓｉ＿ｅｑｕｉｌｉｂｒｉｕｍｐｒｏｂｌｅｍＧＱＥＰ (Ｔ ,Ａ ,ψ)ｉｓｔｏｆｉｎｄ ^ｘ∈Ｘｓｕｃｈｔｈａｔ^ｘ∈Ａ( ^ｘ) ,ψ( ^ｘ ,Ｔ^ｘ ,ｙ)≤ 0…     

Fixed point theorems of random set-valued mappings and their applications

In this paper, first we show several new random fixed point theorems for random set-valued mappings and for a system of random set-valued mappings. Then, some applications of our results are given for the existence and uniqueness of random solution for a system of nonlinear random integral and differential equations. Our theorems improved and generalize many recent findings in [4–7, 9, 11–17].     

PM-空间内映射半群的公共不动点定理

Bharucha-Reid指出对概率度量空间(简记为PM-空间)内映射不动点理论的研究是有实际意义的。近十几年来,已有许多人从事这一方向的研究。 最近我们在[2]中将Jungck和Fisher关于完备距离空间内交换映射的公共不动点定理改进并推广到了PM-空间,从而使Sehgal;Bharucha-Reid的结果成为我们的定理的特例。本文是[2]的继续。我们将进一步研究PM-空间内映射半群的公共不动点的存在唯一性,将Machuca,Cicic和Das,Naik的重要结果改进并推广到PM-空     

随机收缩和随机算子方程的解

<正> §1.引言 最近Lee和Padgett推广Altman的收缩理论,引入了随机收缩概念,得到了随机收缩理论的若干结果.这些结果对于获得随机算子方程解的存在唯一性及解的近似方法提供了极其有用的工具.我们知道,随机算子方程常常产生于生物、物理、工程和系统科学等应用学科之中.因此,对随机收缩理论的进一步研究将是很有意义的. 在本文中,我们将引入比[1,2]更一般的随机收缩概念,讨论具有随机收缩的更一般的随机集值和点值算子方程解的存在唯一性和解的近似.我们的定理进一步改进和推广了[1,2,4]中某些主要结果和其他许多已知结果.     

H—空间的覆盖性质及其应用

我们得到了Ｈ－空间闭（开）覆盖性质的几个定理，改进和推广了Ｓｐｅｒｎｅｒ，Ｋｌｅｅ，Ａｌｅｘａｎｄｒｏｆｆ－Ｐａｓｙｎｋｏｆｆ，Ｂｅｒｇｅ，Ｇｈｏｕｉｌａ－Ｈｏｕｒｉ，Ｄａｎｚｅｒ－Ｇｒｕｎｂａｕｍ－Ｋｌｅｅ，Ｋｙ Ｆａｎ，ｓｈｉｈ－Ｔａｎ，Ｈｏｒｖａｔｈ和Ｌａｓｓｏｎｄｅ等人的相应结果。作为应用，我们对ｌ．ｃ．－空间内的下半连续集值映象证明了一个几站不动点定理并且推广吉洪诺夫不动点定理到ｌ．ｃ．