扩张型随机算子的随机不动点定理和Caristi不动点定理的随机类比

扩张型随机算子的随机不动点定理和Caristi不动点定理的随机类比 SOME RANDOM FIXED POINT THEOREMS FOR EXPANSIVE RANDOM OPERATORS AND A RANDOM VERSION OF CARISTI FIXED POINT THEOREM 侯友良 Hou Youliang 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 关于压缩型和非扩张型随机算子的随机不动点定理,已有很多结果,但关于扩张型随机算子的随机不动点定理,目前文献中尚未见到。本文对具有随机定义域的扩张型随机算子证明了两个随机不动点定理。本文还对一族依赖于参数的偏序集证明了可测的极大元映射的存在性引理,并用之证明了重要的Caristi不动点定理的随机类比。 In this paper, we proved two random fixed point theorems for expansive random operators with stochastic domain. On the otherhand, we proved the existence of the measurable maximal element mapping for a family of partially ordered sets and then we proved a random version of Caristi fixed point theorem. 扩张型随机算子 随机不动点 随机定义域 可分的随机算子 偏序集 Caristi不动点定理 expansive random operator random fixed point stochastic domain seperable random operator partially ordered set caristi fixed point theorem 1989-03-01 2021-04-01 3