Generalization of some inequalities using Lidstone interpolation via diamond integrals

Abstract

In present paper, several inequalities involving Csisz´ar divergence are established by utilizing diamond integrals and Lidstone interpolation polynomials. Consequently, new and generalized inequalities are yields. The functions involved in these inequalities are higher order convex functions. Inequalities involving Shannon entropy, Kullback-Leibler discrimination, triangle distance and Jeffrey’s distance, are studied as particular instances with the help of specially chosen convex functions. The main findings are also discussed for some special time scales (both discrete and continuous). Many existing results are also obtained which established the link with existing literature.