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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 596216, 13 pages
http://dx.doi.org/10.1155/2012/596216
Research Article

A Rogalski-Cornet Type Inclusion Theorem Based on Two Hausdorff Locally Convex Vector Spaces

Department of Mathematics, College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210046, China

Received 30 December 2011; Accepted 21 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Yingfan Liu and Youguo Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Rogalski-Cornet type inclusion theorem based on two Hausdorff locally convex vector spaces is proved and composed of two parts. An example is presented to show that the associated set-valued map in the first part does not need any conventional continuity conditions including upper hemicontinuous. As an application, solvability results regarding an abstract von Neumann inclusion system are obtained.