【摘要】 设K为Hausdorff局部凸拓扑线性空间E的非空紧凸子集,f为K×E上连续实值函数,对每个x∈K,f(X,·)为E上凸函数。设F为K到CC(E)中的上半连续映射。本文证明了:如果对于不属于F(x)的每个x∈K,一切的u∈F(x),存在一个y∈cl(I(K,x)),使得f(x,y—u)<f(x,x—u)。则F在K内有不动点。同时,利用凸函数的次梯度,讨论了不动点的存在性。更多还原

【Abstract】 Let K be a non-empty compact convex subset of a locally convex Haus-dorff topological vector space E, and f a continuous real-valued functionon K×E such that for each x∈K, f(x,.) is a convex function on E, Let F:K→cc (E) be upper semi-continuous, In this note, we prove F has afixed point in K on condition that for each x in K, if x?F(X)and allu∈F(x), there exists y∈cl (I(K,x))such that f(x,y-u)<f(x,x-u), In addi-stion, we discuss the existence of fixed point by using the concept ofsubgradient of a convex function.更多还原