序Banach空间非混合单调二元算子不动点的存在唯一性及应用  

Existence and Uniqueness of Fixed Points for Mixed Non-Monotone Binary Operators in Ordered Banach Spaces and Its Applications

作　　者：张培国[1,2] 刘立山[1] 

机构地区：[1]曲阜师范大学数学科学学院,曲阜273165 [2]菏泽学院初等教育系,菏泽274000

出　　处：《数学学报（中文版）》2010年第1期55-60,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10771117);高等学校博士点科研基金(20060446001);山东省自然科学基金(Y2007A23);曲阜师范大学博士科研启动经费(Bsqd2007040)

摘　　要：利用锥理论和Banach压缩映象原理在更一般的条件下建立了序Banach空间中一类非混合单调二元算子不动点的存在唯一性定理,并应用到Banach空间中二阶非线性Volterra型微分-积分方程初值问题,改进并推广了已有的一些结果.By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness theorem of fixed points for mixed non-monotone binary operators in ordered Banach spaces are investigated under more general condition. As an application, an existence and uniqueness theorem of solutions for initial value problems of second order nonlinear integro-differential equations of Volterra type in Banach spaces is given. The results presented here improve and generalize some known results.

关 键 词：锥理论 非混合单调二元算子 算子不动点 

分 类 号：O177.91[理学—数学]