巴拿赫代数上锥b-距离空间中压缩映射不动点定理Fixed point theorems of contraction mapping in cone b-metric spaces with Banach algebra
李文娟,薛西锋
摘要(Abstract)：
给出了巴拿赫代数上锥b-距离空间的概念,利用迭代法探究了巴拿赫代数上锥b-距离空间中压缩映射不动点定理,证明了广义利普希茨映射在没有正规性的条件下,仍存在不动点并且是唯一的.
关键词(KeyWords)： 巴拿赫代数上锥b-距离空间;广义利普希茨映射;不动点定理;c-序列
基金项目(Foundation): 陕西省自然科学基金(2012JM1017)
作者(Author): 李文娟,薛西锋
参考文献(References)：
- [1]Liu H,Xu S Y.Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings[J].Fixed Point Theory and Applications,2013,DOI:10.1186/1687-1812-2013-320.
- [2]Xu S Y,Stojan R.Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality[J].Fixed Point Theory and Applications,2014,DOI:10.1186/1687-1812-2014-102.
- [3]Huang H,Xu S Y.Fixed point theorems of contractive mapping in cone b-metric spaces and applications[J].Fixed Point Theory and Applications,2013,DOI:10.1186/1687-1812-2013-112.
- [4]Jankovic S,Kadelburg Z,Radenovic S.On cone metric spaces:a survey[J].Nonlinear Analysis,2011,4(7):2591-2601.
- [5]Hussian N,Shah M H.KKM mappings in cone b-metric spaces[J].Comput.Math.Appl.,2011,62(4):1677-1684.
- [6]Dordevic M,Doric D,Kadelburg Z,et al.Fixed point results under c-distance in tvs-cone metric spaces[J].Fixed Point Theory Appl.2011,DOI:10.1186/1687-1812-2011-29.