Essential Method Of Random Fixed Point Theorems For M(?)nch-Type Maps

The research on fixed point theory is an important subject.The essential approach for Monch-type maps fixed point theorem in Banach spaces and the random fixed point theorem for Monch-type random operator in Polish spaces are discussed in the paper.By means of definition of essential,we give the essential theorem in order to discuss the fixed point theorem for Monch-type maps.Then we discuss random fixed point theorem for Monchtype random operator in Polish spaces which is separable.In Banach spaces,we prove the constant operator meet the condition of Monch-type and come to a conclusion about essential of the constant operator based on fixed point theorem of Monch.Take advantage of definitions and construction of function,we reach the essential theorem of Monch-type maps with some condition.Finally we infer existence of fixed point on Monch-type maps in Banach spaces.In Polish spaces,we randomize the definition of essential in Banach spaces and provide the theorem and proof of the Monch-type random operator.Then we prove the essential of the randomized theorem which is similar in Banach spaces by used of the operator's construction.Finally we get conclusion about the existence of Monch-type random operator in Polish spaces.