On Fixed Point Theorems Of Several Classes Operators And Their Applications

This article has been based on the results at home and abroad, and originate from the the cone theory and properties, starting in-depth study of fixed point for several classes of operators without compactness and continuity and concave or convex conditions in Banach spaces, mainly including fixed point theorems of a class of increasing operators and applications, fixed point theorems of a class of mixed montone operators, fixed point theorems of a class of ordered contractive maps.The main research content of this thesis are:(1) By using the cone theory and non-symmetry interative method, it is studied existence, uniqueness and convergence for iterative sequence of fixed points theorems of a class of increasing operators without continuity and compactness conditions. Finally, we apply the result to Hammerstein nonlinear integral equations on R N.(2) In Banach space, we study the fixed points theorems of a class of mixed monotone operators without continuity and compactness conditions in the normal cone limit. Then the fixed point theorems of this kind of operators are further discussed without the normal cone limit. The results presented here improve and generaliz some corresponding results.(3) Using the cone theory, partial order method and monotone iterative techniques in ordered Banach space, some fixed point theorems of a class of ordered contractive mappings are discussed. The obtained results extend and improve the related know works in the literature.