伪度量空间中第七类压缩型映象的不动点定理  

Fixed Point Theorem for the Seventh Class Contraction Type Mappings in Pseudo-metric Space

作　　者：向长合[1] 罗纳 

机构地区：[1]重庆师范大学数学学院,重庆401331 [2]重庆市第六十六中学,重庆404000

出　　处：《重庆师范大学学报（自然科学版）》2015年第3期68-71,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11171363)

摘　　要：通过将度量空间定义中的三角不等式条件减弱为d(x,y)≤Md(x,z)+d(z,y)对非空集合X中的所有x,y,z成立,其中,M≥1是一个常数,引入了伪度量空间,并通过实例说明伪度量空间是对度量空间的真推广。在完备的伪度量空间中,证明了第七类压缩型映象存在唯一不动点,并且,其迭代序列收敛于此唯一不动点。进一步,对第六类压缩型映象给出了迭代序列逼近于不动点的误差估计。This paper introduces pseudo-metric space by weakening the triangle inequality condition in the definition of metric space as d（x,y）≤Md（x,z）＋d（z,y） holds for all x,y,z∈X, where M≥1 is a constant. An example in this paper shows that the class of metric spaces is a proper subset of the class of pseudo-metric spaces. In a complete pseudo-metric space, it is proved that the sev- enth class contraction type mapping has a unique fixed point and the iterative sequence converges to the unique fixed point. Further- more, the error estimates for the sixth class contraction type mapping are given.

关 键 词：不动点 伪度量空间 第七类压缩型映象 误差估计 

分 类 号：O177.91[理学—数学]