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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 105617, 4 pages
http://dx.doi.org/10.1155/2013/105617
Research Article

The Relationship between Two Kinds of Generalized Convex Set-Valued Maps in Real Ordered Linear Spaces

College of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

Received 12 March 2013; Accepted 14 May 2013

Academic Editor: Graziano Crasta

Copyright © 2013 Zhi-Ang Zhou. 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 new notion of the ic-cone convexlike set-valued map characterized by the algebraic interior and the vector closure is introduced in real ordered linear spaces. The relationship between the ic-cone convexlike set-valued map and the nearly cone subconvexlike set-valued map is established. The results in this paper generalize some known results in the literature from locally convex spaces to linear spaces.