Banach空间中非线性二元算子方程组的迭代求解及其应用  

Iterative solutions of systems of nonlinear two binary operator equations in Banach spaces and applications

作　　者：康平[1] 姚建丽[2] 

机构地区：[1]山东大学数学与系统科学学院,山东济南250100 [2]山东建筑大学理学院,山东济南250101

出　　处：《商丘师范学院学报》2007年第12期26-30,共5页Journal of Shangqiu Normal University

基　　金：国家自然科学基金资助项目(10471075);山东大学数学与系统科学学院基金资助项目(306001)

摘　　要：在较弱的条件下,利用非线性泛函分析中的锥理论和单调迭代的方法,首先建立了Banach空间中的一类新的非线性二元算子方程组解的存在唯一性定理,并给出了逼近解的迭代序列的误差估计式;然后作为应用,得到了Banach空间中的Volterra型一阶非线性积分-微分方程组初值问题的解,改进并推广了最近的一些结果.In this paper, by using the cone theory and monotone iterative technique in nonlinear functional analysis, the existence and uniqueness throrem of solutions for a class of systems of new nonlinear two binary operator equations in Banach spaces under weaker conditions is established. The error estimate of the iterative sequences of approximation solutions is given. And then, as an application, the solutions of the initial value problem for systems of first order integro-differential equations of Volterra type in Banach spaces are obtained. The results obtained here improve and extend some recent results.

关 键 词：锥 BANACH空间 二元算子 算子方程组 

分 类 号：O175.8[理学—数学]