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 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 罗婷*,朱传喜 LUO Ting,ZHU Chuanxi 南昌大学数学系, 南昌, 江西, 330031 Department of Mathematics, Nanchang University, Nanchang, Jiangxi, 330031, P. R. China 收稿日期: 2014-01-04 出版日期: 2015-07-25 DOI: 10.11845/sxjz.2014003b
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 摘要 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$$\left\{\!\!\begin{array}{ll} T_1(x,y,z)=x, \\T_2(x,y,z)=y, \\T_3(x,y,z)=z\end{array}\right.$$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. 关键词 ： 非混合单调算子,  正规再生锥,  Banach压缩映射原理 Abstract：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. Key words： generating normal cone    Banach contraction mapping principle 基金资助:国家自然科学基金资助项目 (No. 11361042, No. 11071108, No. 11326099), 江西省自然科学基金资助项目 (No. 20132BAB201001, No. 2010GZS0147),江西省教育厅青年基金(No. GJJ13012)和赣鄱英才555工程''领军人才项目.
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