序Banach空间中非混合单调三元算子方程(组)解的存在唯一性

Existence and Uniqueness of Solutions for (Systems of) Mixed Non-monotone Tripled Operator Equations in Ordered Banach Spaces

本文在序Banach空间中建立了再生正规锥条件下的非混合单调三元算子方程组{T_1(x,y,z)=x,T_2(x,y,z)=y,T_3(x,y,z)=z}以及三元算子方程T(x,x,x)=x解的存在唯一性定理,所得结果推广了已有文献中的二元算子方程(组)解的存在唯一性定理.

In this paper, we establish the existence and uniqueness theorems of solutions for a class of systems of mixed non-monotone tripled operator equations as well as a tripled operator equation satisfying generating normal cone condition in ordered Banach spaces. The obtained results generalize the existence and uniqueness theorems of solutions for binary operator equations in the corresponding literatures.