LEI Ming,WU Ding-ping.Fixed Point Theorems Concerning New Type Cyclic Maps in Complete B-metric-like Spaces[J].Journal of Chengdu University of Information Technology,2017,(01):82-85.[doi:10.16836/j.cnki.jcuit.2017.01.014]
完备拟b度量空间中循环映射的一些不动点定理
- Title:
- Fixed Point Theorems Concerning New Type Cyclic Maps in Complete B-metric-like Spaces
- 文章编号:
- 2096-1618(2017)01-0082-04
- 分类号:
- O177.91
- 文献标志码:
- A
- 摘要:
- 在非线性分析中,不动点定理的研究是一个重要的领域。为引进新的不动点定理,首先给出Alghamdi的拟b度量空间定义及偏序拟b度量空间的定义。其次定义一对半循环映射的概念,并利用这种半循环映射及泛函分析或者非线性分析中类似于压缩映射的方法定义了两种新的循环映射:LW型循环映射和WL型循环映射。利用这两种映射证明一些不动点定理。最后,证明这些不动点定理在偏序化的拟b度量空间中同样成立,并且通过构造一个离散的完备的拟b度量空间中的例子说明LW型映射是有效的。
- Abstract:
- The research of Fixed point theorems is a important field in nonlinear analysis. First, for the purpose of introducing new fixed point theorems, we give the definitions of b-metric-like spaces which is introduced by Alghamdi and the definitions of partially ordered b-metric-like spaces. Second, we introduce the semicyclic pair map. We define two new cyclic maps with the semicyclic pair map and contraction maps in functional analysis or nonlinear analysis: LW-type and WL-type cyclic maps. We prove some fixed point theorems for such maps. At last, we prove that these fixed point theorems are right too in the partially ordered b-metric-like spaces. And we construct a example in discrete complete b-metric-like spaces to illustrate our main results.
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