Professor Iosif Pinelis (Math) published a paper, “Relationships Between the First Four Moments”, in the American Mathematical Monthly 122 (2015) 479–481, which is available to read online.
Professor Iosif Pinelis (Math) published Exact Upper and Lower Bounds on The Difference Between The Arithmetic and Geometric Means, on Cambridge Journals Online Bulletin of the Australian Mathematical Society, first view;
You can read the paper.