The preservation of the convexity of functions (Q1898977)

The authors define a class of generalized convex functions, closed under the integral operator given by \[ W_g(f)(x)= \int^x_0 y'(x) f(t) dt/[g(t)- g(0)],\quad W_g(f)(0)= 0, \] and offer the result that only multiples of powers belong to the class.