Several new cyclic Jensen type inequalities and their applications

We present some fundamental results and definitions regarding Jensen’s inequality with the aim of obtaining new generalizations of cyclic refinements of Jensen’s inequality from convex to higher order convex functions using Taylor’s formula. We discuss the monotonicity of functionals for n-convex functions at a point. Applications of our work include new bounds for some important inequalities used in information theory. © 2019, The Author(s).