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2012 On Semi- ( B , G ) -Preinvex Functions
Xiaoling Liu, D. H. Yuan
Abstr. Appl. Anal. 2012: 1-13 (2012). DOI: 10.1155/2012/530468


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.


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Xiaoling Liu. D. H. Yuan. "On Semi- ( B , G ) -Preinvex Functions." Abstr. Appl. Anal. 2012 1 - 13, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1237.26010
MathSciNet: MR2872315
Digital Object Identifier: 10.1155/2012/530468

Rights: Copyright © 2012 Hindawi


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