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Journal of Applied Mathematics
Volume 2012, Article ID 168172, 12 pages
Research Article

A Class of -Semipreinvex Functions and Optimality

1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2School of Economics and Management, Tsinghua University, Beijing 100084, China

Received 31 May 2012; Accepted 27 October 2012

Academic Editor: Xue-Xiang Huang

Copyright © 2012 Xue Wen Liu et al. 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.


A class of -semipreinvex functions, which are some generalizations of the semipreinvex functions, and the -convex functions, is introduced. Examples are given to show their relations among -semipreinvex functions, semipreinvex functions and -convex functions. Some characterizations of -semipreinvex functions are also obtained, and some optimality results are given for a class of -semipreinvex functions. Ours results improve and generalize some known results.