Popoviciu's Inequality For N-convex Functions

This book is in the memory of Professor Tiberiu Popoviciu who gave the characterization of convex function in his famous Popoviciu's inequality 50 years ago. In the present book, the first part comprises of literature review of Popoviciu's inequality up to 50 years and then generalization of Popoviciu's inequality for convex functions is given. The later part deals with generalizations of Popoviciu's inequality for n-convex functions Via different interpolation polynomials. New upper bounds are introduced for the identities related to the generalization of the Popoviciu's inequality using Cebysev functional. Some results relating to the Gruss and Ostrowski type inequalities are constructed. At the end of each section we investigate the n-exponential convexity of new functionals and give related results.