On coincidence points for vector mappings

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• 作者：E. S. Zhukovskiy
• 关键词：system of operator equations ; vector covering mappings of metric spaces ; coincidence points ; n ; fold fixed points
• 刊名：Russian Mathematics (Iz VUZ)
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：60
• 期：10
• 页码：10-22
• 全文大小：698 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-810X
• 卷排序：60

文摘

For mappings acting in the product of metric spaces we propose a concept of vector covering. This concept is a natural extension of the notion of covering formappings inmetric spaces. The statements on the solvability of systems of operator equations are proved for the case when the left-hand side of an equation is a value of a vector covering mapping and the right-hand side is Lipschitzian vector mapping. In the scalar case the obtained statements are equivalent to the coincidence point theorems by A. V. Arutyunov. As an application, we prove a statement on the existence of n-fold coincidence points and obtain estimates of the points. The sufficient conditions for n-fold fixed points existence, including the well-known theorems on double fixed point, follow from the obtained results.