随机单调算子的满射性及应用

Property of Surjection for Monotonic Random Operator and Its Application

研究Banach空间中的随机单调算子,建立了连续随机单调算子的随机锐角原理、随机满射定理、随机双射定理及Hilbert空间上的一类连续随机算子的新的随机不动点定理,并应用随机强单调算子理论讨论了随机Hammerstein积分方程随机解的存在唯一性.

The monotonic random operators are studied in Banach spaces. The random acute angle principle, random surjection theorem and random bijection theorem for the continuous monotonic random operators are established. Some new random fixed point theorems for continuous random operators in Hilbert spaces are obtained. Also, the existence of unique random solution for the random Hammerstein type integral equation is discussed by applying the theory of strongly monotonic random operator.