New Hadamard-type estimations of cyclic Jensen functionals via Taylor’s formula - S. I. Butt; T. Rasheed; Ð. Pečarić; J. Pečarić (Journal of Inequalities and Applications)
Abstract Cyclic refinements of Jensen inequalities are quite useful to construct new cyclic information inequalities. Thus, in this paper, we construct cyclic Jensen functionals from the differences of cyclic refinements of Jensen inequalities and then formulate new Hadamard-type upper and lower estimates by employing Taylor’s formula. We utilize the theory of n-times differentiable convex functions. The validity and correctness of the bounds obtained are justified by several concrete examples. Moreover, we give applications of our results to give a variety of cyclic entropic estimations in information theory.