Convexity of elementary functions with applications to inequalities

holds for all λ ∈ [0, 1] and x, y ∈ I . If instead in (1) we have , such a function is concave. In most textbooks convexity is treated within differential calculus. However, we will see how one can single out convex functions among the basic elementary ones without exploiting differential calculus. This will be achieved by using several inequalities and simple assertions. In addition, some elementary convex functions, as it was pointed out in Jensen’s