一类非混合单调算子方程组解的存在唯一性  

Existence and Uniqueness of Solutions for a System of Non-mixed Monotone Operator Equations

作　　者：马艳 翟成波[1] MA Yan;ZHAI Cheng-bo(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《数学的实践与认识》2023年第8期210-221,共12页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(201901D111020)。

摘　　要：研究了半序Banach空间上一类新的非混合单调算子方程组,主要利用锥理论、混合单调算子理论以及单调迭代方法,给出了这类算子方程组解的存在唯一性与收敛于算子方程组解的逼近迭代序列和误差估计,将单一非混合单调算子方程情形下的结论推广到算子方程组的结果,对文献中相关结论做进一步的推广.In this paper,a new system of non-mixed monotone operator equations in ordered Banach spaces is studied.By using cone theory,mixed monotone operator theory and monotone iterative method,the existence and uniqueness of solutions for this system,and the approximation iterative sequence and error estimate of the solution for the operator equations are given.The results of single non-mixed monotone operator equation are extended to systems of operator equations,which extend some related conclusions in literature.

关 键 词：算子方程组 混合单调算子 不动点 单调迭代方法 存在唯一性 

分 类 号：O175[理学—数学]