1. Warm-up problem set
1.1 Applications
1.2 Solutions
2. Starting from some special fourth degree inequalities
2.1 Main results
2.2 Solutions
2.3 Another related inequalities
2.4 Solutions
3. Inequalities with right convex and left concave functions
3.1 Inequalities with right convex functions
3.2 Inequalities with left concave functions
3.3 Inequalities with left concave-right convex functions
3.4 Applications
3.5 Solutions
4. On Popoviciu's inequality
4.1 Introduction
4.2 Applications
4.3 Solutions