Two Kinds Of Fixed Points Theorems And Their Applications

In complete metric spaces,a fixed point theorem of contractive mapping with gen-eralized altering distance functions is established.Applying our result to the first-order ordinary differential equation with periodic boundary value condition,we obtain sufficient conditions for the existence of unique solution of the equation.Our results are weaker than the existing results and completely remove the condition for the existence of the lower solution.On the other hand,by using the concept of asymptotic regularity,the fixed point theorem of Reich-type contractive is extended from metric space to b-metric space.This result is an improvement and supplement to the previous results.According to our results,Reich-type and weak Ciric type contraction fixed point theorems are deduced in b-metric spaces.