The Existence of the Solutions of Some Non-monotone Operator Equations in Banach Space

By using the core theory and non-symmetric iterative method,it is studied the existence uniqueness of solutions of some operator equations without monotone and continuity and compactness conditions in Banach spaces.And the iterative sequences which converge to solution of operator equations and the error estimates are also given.The results presented here improve and generalize some corresponding results for increasing(decreasing) operator equations.