混合单调算子的不动点定理及其应用  

Fixed Point Theorems of Mixed Monotone Operators and Their Applications

作　　者：段华贵[1] 李国祯[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330027

出　　处：《江西师范大学学报（自然科学版）》2003年第4期356-360,共5页Journal of Jiangxi Normal University(Natural Science Edition)

摘　　要：首先利用锥理论和非对称迭代方法得到了若干混合单调算子,增(减)算子的不动点定理,推广和改进了吴焱生和李国祯文献中的相关结果.其中,我们去掉了此文中定理3 1的条件(ⅱ),同样得到了一类α-凹和(-α)-凸的混合单调算子的不动点定理.最后,将所得到的结果应用于RN上的Hammerstein积分方程之中.Using the cone theory and non-symmetric iterative methods,we obtain some fixed point theorems for mixed monotone operators,increasing operators and decreasing operators.These improve and extend some relative conclusions in paper of WU and LI.Secondly we drop out the condition (ⅱ) of Theorem 3.1 in paper of Wu Yan-sheng and LI Guo-zhen get a fixed point theorem for mixed monotone operators with α-concave and (-α)-convex conditions.Finally,we apply the obtained results to Hammerstein integral equations on R^N.

关 键 词：混合单调算子 不动点定理 锥理论 非对称迭代方法 a-凹算子 (-a)-凸算子 

分 类 号：O177.91[理学—数学]