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--preinvex functions, strictly semi--preinvex functions and explicitly semi--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.
"On Semi--Preinvex Functions." Abstr. Appl. Anal. 2012 1 - 13, 2012. https://doi.org/10.1155/2012/530468