混合单调算子不动点定理的拓展研究  

Research on Fixed-Point Theorem for a Type of Mixed Monotone Operators

作　　者：尚珍珍 张小勇[1] 寇海荣 SHANG Zhenzhen;ZHANG Xiaoyong;KOU Hairong(Department of Intelligence and Automation,Taiyuan University,Taiyuan 030032,China)

机构地区：[1]太原学院智能与自动化系,山西太原030032

出　　处：《太原学院学报（自然科学版）》2022年第1期44-47,共4页Journal of TaiYuan University:Natural Science Edition

基　　金：山西省高等学校科技创新项目(2020L0718);山西省高等学校教学改革创新项目(J2020383)。

摘　　要：巴拿赫空间中混合单调算子的不动点理论已经有了广泛的研究,并且有很多应用。混合单调算子是一类非常重要的算子,广泛存在于非线性积分方程和微分方程的研究中。研究拓展了一类混合单调算子的不动点定理,对压缩条件的不等式两侧都分别进行了改进,应用对称性将不等式左侧单项变成两项和的形式,不等式右侧用函数进行限制,其适应范围更广。在完备度量空间内通过证明柯西列的收敛性,进而得出不动点定理,并应用到非线性积分方程中。The fixed-point theorem of mixed monotone operators in Banach spaces has been extensively studied and widely applied.As a very important type of operators,mixed monotone operators are widely used in the study of nonlinear integral equations and differential equations.In this paper,the fixed-point theorem of a type of mixed monotone operators was studied and extended,and both sides of the inequality under the compression condition were improved.The symmetry was used to change the single terms on the left side of the inequality into the sum of two items,and the right side of the inequality was restricted by a function,making the inequality more widely used.By proving the convergence of Cauchy sequence in complete metric space,the fixed-point theorem was obtained and thus applied to nonlinear integral equation.

关 键 词：耦合不动点 混合单调算子 半序集 柯西定理 

分 类 号：O17[理学—数学]