局部凸值矩形度量空间与Kannan的不动点定理
Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem
摘要：
引入了矩形TVS-锥度量空间，并证明了Kannan的不动点定理.两种方法的证明。首先利用空间本身的结构用直接法证明了定理。其次，我们使用了杜伟世最近在[A note on cone metric不动点theory and its equivalents，{Nonlinear Analysis}，72（5），2259 -2261（2010）]中使用的非线性标量化。证明了Banach压缩原理在锥度量空间和一般度量空间中的等价性。证明过程中对局部凸拓扑向量空间的锥不作任何正规性假设，推广了已有的结果。
英文摘要：
Rectangular TVS-cone metric spaces are introduced and Kannan's fixed point theorem is proved in these spaces. Two approaches are followed for the proof. At first we prove the theorem by a direct method using the structure of the space itself. Secondly, we use the nonlinear scalarization used recently by Wei-Shih Du in [A note on cone metric fixed point theory and its equivalence, {Nonlinear Analysis},72(5),2259-2261 (2010).] to prove the equivalence of the Banach contraction principle in cone metric spaces and usual metric spaces. The proof is done without any normality assumption on the cone of the locally convex topological vector space, and hence generalizing several previously obtained results.
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