The concepts and of concave and quasi-concave functions is still predominant mat hematical techniques used by economists to study firm and consumer theory,and th e quasi-concavities of function are obtained much deeper researches in it at tim e.
凹函数和拟凹函数的概念及其性质一直是经济学家使用来研究厂商理论和消费者理论的主要数学技术,函数拟凹性也在其中得到许多深刻的研究。
In this paper, we introduce the concept of closed function, obtain two sufficient and necessary conditions that the closed function is a quasiconcave function, and study the relation between quasiconcave function, strictly quasiconcave function and strongly quasiconcave function.
研究了一类函数成为拟凹函数的充分必要条件，讨论了拟凹函数与严格拟凹函数和强拟凹函数的关系。
And then,by introducing the concept of weakly quasiconcave function,and replacing quasiconcave function by weakly quasiconcave function,a new existence theorem of Nash equilibrium point for game theory is deduced.
推广了Fan-Glicksberg不动点定理,引入弱拟凹函数的定义,用弱拟凹函数代替拟凹函数,弱化Nash平衡点存在的条件,得出一个新的判定定理,并举例说明了它的实用性。
