一类新反向混合单调算子方程组解的存在惟一性  

The Existence and Uniqueness of Solutions of Some New Anti-mixed Monotone Operator System of Equations

作　　者：徐华伟[1] 王大鹿[2] 

机构地区：[1]商丘师范学院数学与信息科学学院,河南商丘476000 [2]黄河水利职业技术学院基础部,河南开封475003

出　　处：《四川师范大学学报（自然科学版）》2013年第4期578-582,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：河南省自然科学基金(112300410268)资助项目

摘　　要：在非线性算子的研究中,一般都要考虑到算子的紧性、凹凸性、连续性等,而在锥满足正规的前提下,可以忽略或者弱化算子附加的一些条件.运用锥与半序理论和非对称迭代方法,讨论半序Banach空间一类反向混合单调算子方程组解的存在惟一性,给出了迭代序列收敛于解的误差估计,并推广讨论了非反向混合单调算子方程组解的存在惟一性,所得结果改进和推广了混合单调算子方程某些已知相应结果,进一步完善了非线性算子的理论研究.In the study of nonlinear operators the tightness,convexity and continuity of operators are normally taked into account.When the cone is normal,some of these properties attached to operators can be ignored or weakened.Using the cone,partial order theory and non-symmetry iteration method,the existence and uniqueness to solutions to a class of anti-mixed monotone operator system of equations in Banach spaces are proved.The iteration sequences which converge to solution of operator equations and the error estimates are also given.As a generaliaztion,the existence and uniqueness of solutions of non-anti-mixed monotone operator system of equations are also discussed.The results presented here improve and generalize some corresponding results for mixed monotone operators.

关 键 词：锥与半序 反向混合单调算子 非对称迭代 不动点 

分 类 号：O177.91[理学—数学]