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Kantorovich’s Fixed Point Theorem and Coincidence Point Theorems for Mappings in Vector Metric Spaces
Set-Valued and Variational Analysis ( IF 1.6 ) Pub Date : 2021-06-16 , DOI: 10.1007/s11228-021-00588-y
Aram V. Arutyunov , Evgeny S. Zhukovskiy , Sergey E. Zhukovskiy , Zukhra T. Zhukovskaya

The fixed points and coincidence points of mappings of v-metric spaces, i.e., sets on which a vector metric is defined, are investigated. The values of such a metric are elements of a cone of a Banach space rather than real nonnegative numbers. Analogs of Kantorovich’s theorems on the existence and uniqueness of a fixed point and the convergence of an iteration sequence to this point are obtained. Conditions for the existence of a coincidence point of two mappings are obtained. The results obtained are generalized to the case of set-valued mappings.



中文翻译:

用于向量度量空间映射的 Kantorovich 不动点定理和重合点定理

研究了v-度量空间映射的不动点和重合点,即定义了向量度量的集合。这种度量的值是巴拿赫空间锥体的元素,而不是实数非负数。得到了关于不动点的存在性和唯一性以及迭代序列到该点的收敛性的 Kantorovich 定理的类比。得到两个映射重合点存在的条件。获得的结果被推广到集值映射的情况。

更新日期:2021-06-17
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