  In this paper we derive some Edmundson-Lah-Ribari\v{c} type inequalities for
positive linear functionals and 3-convex functions. Main results are applied to
the generalized f-divergence functional. Examples with Zipf Mandelbrot law are
used to illustrate the results. In addition, obtained results are utilized in
constructing some families of exponentially convex functions and Stolarsky-type
means.
