Convex conjugate
Convexity
For two functions 
and 
and a number 
the convexity relation
holds. The 
operation is a convex mapping itself.
The infimal convolution (or epi-sum) of two functions f and g is defined as
Let f1, …, fm be proper, convex and lsc functions on R. Then the infimal convolution is convex and lsc (but not necessarily proper), and satisfies