On the convexity of images of nonlinear integral operators

详细信息    查看全文

• 作者：M. Yu. Kokurin
• 关键词：nonlinear integral operator ; multivalued mapping ; image of a set ; closure ; convexity ; quasisolution
• 刊名：Mathematical Notes
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：100
• 期：3-4
• 页码：561-567
• 全文大小：596 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876
• 卷排序：100

文摘

We study continuous nonlinear Urysohn-type integral operators acting from the spaces of vector functions with integrable components to the space of continuous functions. We obtain conditions under which the images of sets defined by pointwise constraints have a convex closure under the action of these operators. The result is used to justify a method of constructive approximation of these images and to derive a necessary solvability condition for Urysohn-type integral equations. A numerical method for finding the residual of equations of this type on the sets under consideration is justified.