Is There A Generalization Of Brouwer's Fixed Point Theorem?

Using krasnoselskii fixed point theorem prove fixed point of a operator in a banach space?

• Answer:

  Krasnoselskii fixed point theorem states that under certain sircumstances the operator has at least one fixed point in a subset of a Banach space. It doesn't say anything about uniqueness of solutions, just existence, but sometimes this is usefull enough, and perhaps you can get uniqueness by some other way. I hope this answers your question