Abstract and Applied Analysis

On Semi-$(B,G)$-Preinvex Functions

Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 530468, 13 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495626

Digital Object Identifier
doi:10.1155/2012/530468

Mathematical Reviews number (MathSciNet)
MR2872315

Zentralblatt MATH identifier
1237.26010

Citation

Liu, Xiaoling; Yuan, D. H. On Semi- $(B,G)$ -Preinvex Functions. Abstr. Appl. Anal. 2012 (2012), Article ID 530468, 13 pages. doi:10.1155/2012/530468. https://projecteuclid.org/euclid.aaa/1355495626

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