



Volume 6, Issue 3, Article 85 






Outer $ \gamma$Convex Functions on a Normed Space



Authors: 
Phan Thanh An, 



Keywords:

Convexity, Epigraph, Jensen inequality, Outer $ gamma$convex set, Outer $ gamma$convex function 



Date Received:

22/03/05 



Date Accepted:

28/06/05 



Subject Codes: 
26A51, 26B25, 52A41.




Editors: 
Alexander M. Rubinov (19402006), 









Abstract: 
For some given positive , a function is called outer convex if it satisfies the Jensen inequality for some satisfying , where . Though the Jensen inequality is only required to hold true at some points (although the location of these points is uncertain) on the segment , such a function has many interesting properties similar to those of classical convex functions. Among others it is shown that, if the infimum limit of an outer convex function attains at some point then this propagates to other points, and under some assumptions, a function is outer convex iff its epigraph is an outer convex set.
















