关于Banach空间中凸泛函的广义次梯度不等式

On the Subgradient Inequality of Convex Functionals in Banach Spaces

本文在前人[1,2 ] 的基础之上 ,以凸泛函的次梯度不等式为工具 ,将Jensen不等式推广到Banach空间中的凸泛函 ,导出了Banach空间中的Bochner积分型的广义Jensen不等式 ,给出其在Banach空间概率论中某些应用 ,从而推广了文献 [3 6

In recent years the theory of convex functionals has been developing very fast.Many results of linear functionals are generalized in convex functionals,based on [1]and [2]in the light of thinking of generlization.In this paper,this paper gives on the subgradient inequality of convex functionals in the Banach spaces and its stochastie analysis applications of convex functionals and their applications,by means of subgraduent inequality of convex functionals thus generalizing the result of [3],[4],[5],[6].