I have a piecewise linear function which is continuous. I am looking for a good way to "smooth" the function at the boundary points. Ideally, I would like a solution that's similar to A. Bellmunt's here:
A smooth function instead of a piecewise function
However, in my case, the slopes between each need not be $0$ or $1$, rather, they can be arbitrary. Futher, I require that the "smoothed" section lie above each piece of my piecewise linear function.
What is the simplest such construction that exists?