Abstract and Applied Analysis
Volume 2013 (2013), Article ID 103864, 7 pages
http://dx.doi.org/10.1155/2013/103864
Research Article

Semistrict -Preinvexity and Optimality in Nonlinear Programming

Z. Y. Peng,1,2 Z. Lin,1 and X. B. Li1

1College of Science, Chongqing JiaoTong University, Chongqing 400074, China
2Department of Mathematics, Inner Mongolia University, Hohhot 010021, China

Received 26 October 2012; Accepted 10 April 2013

Academic Editor: Natig M. Atakishiyev

Copyright © 2013 Z. Y. Peng 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.

Abstract

A class of semistrictly -preinvex functions and optimality in nonlinear programming are further discussed. Firstly, the relationships between semistrictly -preinvex functions and -preinvex functions are further discussed. Then, two interesting properties of semistrictly -preinvexity are given. Finally, two optimality results for nonlinear programming problems are obtained under the assumption of semistrict -preinvexity. The obtained results are new and different from the corresponding ones in the literature. Some examples are given to illustrate our results.