乘积空间中非线性算子的极大极小不动点定理及迭代法*

本文研究了乘积空间中非线性算子的极大极小不动点和迭代法.作为我们结果的推论,一些耦合不动点定理被获得、它们推广了由郭大钧和Lankshmikantham获得的耦合不动点定理.(见Nonlinear Anal、11(1986),623-632)和由兰在[4]、[6]中获得的结果.     

广义强非线性拟补问题*

利用本文中的算法,我们证明了广义强非线性拟补问题解的存在性及由算法产生的迭代序列的收敛性,改进和发展了Noor,Chang-Huang等人的结果.此外,也给出了求广义强非线性拟补问题的近似解的另一更一般的迭代算法并证明了由此迭代格式获得的近似解收敛于此补问题的精确解.     

Iterative process for lipschitz local strictly pseudocontractive mappings

ＩＴＥＲＡＴＩＶＥＰＲＯＣＥＳＳＦＯＲＬＩＰＳＣＨＩＴＺＬＯＣＡＬＳＴＲＩＣＴＬＹＰＳＥＵＤＯＣＯＮＴＲＡＣＴＩＶＥＭＡＰＰＩＮＧＳＤｅｎｇＬｅｉ（邓磊）（ＣｈｏｎｇｑｉｎｇＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ,Ｙｏｎｇｃｈｕａｎ,Ｃｈｏｎｇｑｉｎｇ）Ｄ...     

Fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces and its applications

The author defines a concept of fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces. Using this concept, the author establishes several nonzero fixed point theorems of set-valued -condensing mappings. These theorems extend some known results in [1,2,7,8,9].Projects Supported by the Science Fund of the Chinese Academy of Sciences     

Some coincidence theorems of set-valued mappings

Browder^[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder’s results in several aspects. Recently, H.M. Ko and K.K. Tan^[2,3] generalized Browder’s theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems oj set-valued mappings. They improve and generalize the important results in [1,2,3].     

一般随机不动点定理及其应用

在本文中我们得到了一个一般的随机不动点定理,推广了Engl[4,7]和Bocsan[8]的主要结果.这一定理的有用性在于目前由许多作者用特殊方法得到的随机不动点定理[1,4,5-13]均能利用我们的一般定理(定理1和系1,2)得到,最后给出了我们的定理对随机积分和微分方程的应用.     

Maximal elements of condensing preference maps in locally convex Hausdorff spaces

Two existence theorems of maximal elements of condensing preference maps in locallyconvex Hausdorff spaces are proved which generalize the recent results of Mehta.One ofthem positively answers the Open problem mentioned by Mehta.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications （II）

This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 2003A081 and SZD0406)     

EXISTENCE AND COMPARISON RESULTS OF SOLUTIONS FOR NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS RELATIVE TO WEAK TOPOLOGY

In this paper,we prove several existence theorems of random solutions to nonlinearrandom Volterra integral equations under the weak topology of Banach spaces.Then,asapplications,we obtain the existence theorems of weak random solutions to randomdiffrential equations. Existence of extremal random solutions and a random comparisontheorem for these random equations are also obtained.Our theorems imaprove and extendthe corresponding resulls in [4,5,10,11,12].     

PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS

A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings