一类三元反向混合单调算子不动点定理及其应用Fixed point theorems of a type tripled reverse mixed monotone operator
谢卢梦;薛西锋;
摘要(Abstract)：
利用单调迭代方法、数学归纳法、锥理论方法研究了具有半序的Banach空间反向混合单调算子的不动点的存在性与唯一性,得到的结论推广了反向混合单调算子不动点的存在性与唯一性.最后,将所得到的结论应用于Hammerstein积分方程中.
关键词(KeyWords)： 反向混合单调算子;正规锥;不动点;迭代序列
基金项目(Foundation): 陕西省自然科学基金(2012JM1017)
作者(Authors): 谢卢梦;薛西锋;
参考文献(References)：
- [1]Guo Dajun,Lakskmikantham V.Coupled fixed point of mixed monotone operator with application[J].Nonlinear Analysis,1987,11:623-632.
- [2]孙义静.一类非线性算子方程组的迭代算法及应用[J].浙江大学学报:自然科学版,1999,3:289-294.
- [3]王维娜,薛西锋.混合单调算子对的新不动点定理及应用[J].纺织高校基础科学学报,2014,9:328-331.
- [4]Lakshmikantham V,Ciric L.Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces[J].Nonlinear Anal.,2009,70:4341-4349.
- [5]Marin Borcut.Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces[J].Applied Mathematics and Computation,2012,218:7339-7346.
- [6]Xinsheng Du.New fixed point theorems of mixed monotone operators[J].Applied Mathematics,2014,5:352-357.
- [7]Hojjat Afshari.New tripled fxied point theorems of mixed monotone operators and applicaions[J].Journal of Nanjing University Mathematical Biquarterly,2014,10:174-186.
- [8]孙经先.非线性泛函分析及其应用[M].北京:科学出版社,2007.
- [9]Vasile Berinde,Marin Borcut.Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces[J].Nonlinear Analysis,2011,74:4889-4897.