概率度量空间中集值Caristi定理

SET-VALUED CARISTI'S THEOREM IN PROBABILISTIC METRIC SPACES

本文得到了概率度量空间中的集值Caristi型重合定理、加强形式的集值Caristi不动点定理及Ekeland变分原理,同时还证明了这一加强形式的集值Cariti不动点定理与Ekeland变分原理的等价性.本文所得结果统一和发展了近期一些巳知的重要结果.

In this paper, a set-valued Caristi's type coincidence theorem, a formally stronger set-valued Caristi' s fixed point theorem and an Ekeland' s variational principle in probabilistic metric spaces are obtained. By a simple method we give a direct proof for the equivalence between the Ekeland's variational principle and the formally stronger set-valued's fixed point theorem in probabilistic metric spaces. The results presented in this paper unify and extend some recent important results.