On Semi-(B,G)-Preinvex Functions

We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover,...

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Bibliographic Details
Main Authors: Xiaoling Liu, D. H. Yuan
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/530468
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Summary:We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.
ISSN:1085-3375
1687-0409