Fixed Point Theory Of Some Nonlinear Operators

In this thesis, we investigate the fixed point problem of some nonlinear operators. And we gain some fixed point theorems.In chapter 1, we have studied random couple fixed points of nonlinear random mixed monotone operators ,and derived Some random version of Guo's deterministic couple fixed point theorems for mixed monotone operators.In chapter 2, we have studied semi-closed 1-set contraction operators and generalized Amann's three-solution theorem under the hypothesis of e-continuity.In chapter 3, by virtue of the index for semi-closed 1-set contraction mapping on the unbounded sets(see[9]), some well-known boundary conditions and proper value problems on bounded sets in Banach spaces are extended to the case that is on unbounded sets.In chapter 4, by virtue of the index for semi-closed 1-set contraction mapping on the unbounded sets(see[9]), the fixed point theorem of cone expansion and compression for semi-closed 1-set contraction mapping on an unbounded set is proved in semi-ordered Banach spaces.