H-空间中的不动点理论及相关问题研究

In the item, fixed point and almost fixed point problems of upper semicontinuous multivalued mapping ang lower semicontinuous multivalued mapping, the existence problems of solutions for Ky Fan.implicit variational inequalities and Browder － Hartman － Stampacchia quasi-variational inequalities, minimax problems, proximate selection problems, equilibrium problems of abstract economy (generalized game), optimization problems in H-spaces and fixed point and almost fixed point problems of upper semicontinuous multivalued mapping in hyperconvex metric spaces were studied.The results what we obtained, one part is new and important and another part improves and extends previous some famous results.

本项目通过研究和解决H--空间中上（下）半连续集值映射不动点问题，进一步研究H--空间中抽象经济平衡问题和相关的变分不等式和最优化问题。其意义在于解决十年来引起国内外同行数学家关注的H--空间中未得以解决的上（下）半连续集值映射不动点问题，进而为数砭醚芯咳鹊?---非线性经济模型，建立重要的平衡理论。